Facade
The construction of the west façade began 45 years after the consecration of the choir and in a completely different style from the façades of the transept, which was consequently thoroughly modernised another 40 years later. It was completed around 1250, i.e. at about the time when the Gothic style began in Germany. The façade of the basilica of Saint-Denis, already completed in 1137, and that of the cathedral of Laon (1190) show trends that the building in Paris does not take up. It again offers the traditional box-like appearance with the accentuated horizontal elements, but in precisely calculated, balanced proportions.
The proportions of the façade are based on the arrangement of squares that are interlocked. This builds up a rectangle in the aspect ratio of around 2:3. This was intended to realize the ideal of St. Augustine: an architecture whose proportions were based on musical consonances, which in turn reflect the harmonic order of the universe. The central portal is only slightly prominent compared to the side portals. In this respect, Notre-Dame is retrograde and almost reminiscent of the Norman façade of the monastic church of Saint-Étienne in Caen from 1060, 140 years earlier.
On the other hand, a decisive innovation in façade design was introduced in Paris, namely the royal gallery above the portal zone as a symbol of the union of church and monarchy. The 28 figures represent the kings of Judah. As early as the 13th century, the people considered them to be the kings of France. This row of larger-than-life royal statues was adopted in some of the most important cathedrals after Paris, such as those in Reims and Amiens. The royal figures in the Paris cathedral, however, are all modern interpretations. Their originals - which, after all, commonly represented to the people the claim to power of the French kings - were destroyed during the French Revolution, as were many works of art in Notre-Dame. The figures were replaced by Eugène Viollet-le-Duc during restoration work beginning in 1845. Two of the royal figures feature the facial features of Viollet-le-Duc and Jean-Baptiste Lassus. In 1977, 21 of the 28 original heads were rediscovered. They are now on display at the Musée national du Moyen Âge.
Notre-Dame has important figural portals on both the west façade and the transepts. The three portals of the west façade were heavily restored in the 19th century and only a small part of the original substance remains. When Notre-Dame was rededicated as a temple of reason during the French Revolution, most of the depictions were destroyed or severely damaged. However, as the original programme and appearance were known, the restorers largely kept to the medieval state.
The northern of the three west portals, the Portail de la Vierge, is the oldest. It was built around 1200 and is dedicated to the Virgin Mary. In the tympanum, the pediment above the portal, the so-called coronation of Mary is depicted. The lintel below shows Mary awakened by Christ and being lifted out of her coffin by two angels in the presence of the 12 apostles. The lowest part shows representations of prophets.
The central west portal, the Portail du Jugement dernier, is somewhat later than the Portal de la Vierge. Depictions of the Last Judgement were widespread in the medieval Gothic period and can also be found on portals of other important cathedrals. At the top of the tympanum is Christ depicted as the Judge of the World. Directly below Christ is an angel with a weighing pan, weighing the souls of the deceased. Immediately next to him is a devil who is arguing with the angel about which dead will enter hell (to the right of the devil) and which will enter heaven (to the left of the angel).
The southern side portal, the Portail Sainte-Anne (c. 1230), is the youngest of the three west portals, but has the oldest elements; they date from the 12th century and were used for the tympanum and a lintel. It is named after Saint Anne and also corresponds thematically with the Portail de la Vierge on the other side. In the centre of the tympanum, the Virgin Mary is shown enthroned, holding the blessing baby Jesus on her lap.
· 
Tympanum of the side portal Portail de la Vierge
(northern west façade)
· 
Tympanum of the main portal Portail du Jugement dernier (centre of the west façade)
· 
Tympanum of the side portal Portail Sainte-Anne (southern west façade)
Longwall
The longwall of 1180/1200 is considered a decisive invention in the history of Gothic architecture, initially attributed to the builders of Notre-Dame, Pierre de Montreuil and Jean de Chelles. So far, it is not certain on which building the open longwall was used for the first time. Subsequent enlargements of the window zones, structural damage or restorations have obscured the original condition of many earlier longwalls. In Paris, the struts were initially still installed under the gallery roofs.
Between 1160 and 1180, the first buttresses rising above the aisle roofs were built, possibly not at Notre-Dame but a few hundred metres further on at St Germain-des-Prés. The buttress system of Notre-Dame would therefore have been enlarged and raised later. Exact data are not available here, however.
It is possible that the Parisian flying buttresses were not built until after 1200, after those of Bourges and Chartres, because Notre-Dame de Paris did not have vaults at first, but a wooden ceiling, which is why the problems with lateral thrust hardly existed. The first architect of the Paris cathedral did not yet know how to support such a high vault and left the problem open for later generations. It was not until the second architect was able to build on experience elsewhere that he pulled in the vault and supported it externally with the open buttress. Because of the comparatively earlier start of construction of the entire cathedral in 1163, it was long believed that the buttress had been invented at Notre Dame Cathedral.
Until then, attempts had been made in architecture to divert the vaulting thrust over thick walls or over chapels, side aisles and galleries. There were indeed some preliminary forms of the Gothic flying buttress, e.g. at the Hagia Sophia in Constantinople in the 6th century, or in the ambulatory choirs from about 1160 in Normandy and Île-de-France. But in Paris a completely new idea arose around 1160/80, namely to erect a separate construction for the vaulting thrust next to the actual church, and only this is called Gothic longwall.
With the invention of the buttress as an external support for the vault thrust, a completely new dimension was added to Gothic cathedral construction. Only now was it possible, with the combination of ribbed vault, pointed arch and flying buttress, to direct, concentrate and shift the weight of the church, i.e. above all the weight of the vault and the lateral thrust, to the outside. The outer support system could hardly be seen from the inside. Only now could the Gothic principle of wall dissolution, the transformation of the wall into a translucent, disembodied layer of glass, be properly carried out, as the wall was relieved of much of its supporting function. The interior of the cathedral was now dominated by that much-cited "upwardly striving incorporeality".
This made it possible to build to completely different heights, because the problem of the vault thrust became largely independent of the construction of the interior. Paris also reached with a vault height in the central nave of 32.5 meters a height that had been considered impossible until then. Sens, Noyon and Laon ranged between 22 and 24 metres. Notre-Dame was therefore ten metres higher. The vault height in the Gothic cathedrals of France will still increase up to the absolute maximum of 48 meters in Beauvais.
Grotesques
The famous grotesques of the "Galerie des Chimères", which look down on the city from the upper balustrade (see also Drolerie), have had apotropaic significance since time immemorial, i.e. they were supposed to ward off evil spells. Monsters of all kinds are a peculiarity of Romanesque art. In the 13th century their depiction in favoured places such as the portals declined noticeably, probably due to the strong influence of the Cistercian monks. Thus, in Gothic times, the strange mythical creatures were only placed on the rainwater spouts.
The original gargoyles were removed in the 18th century when some began to crumble due to the effects of the weather and fell 60 metres onto the pavement. The figures are now 19th century copies or re-creations and influenced by Victor Hugo's novel. This is clearly noticeable from close up by the concrete character of the material.
Interior
Notre-Dame is the last large early Gothic cathedral in France and also the last and largest gallery church. The five-nave interior measures just under 130 meters in length and can accommodate about 9000 people. The central nave reaches a height of 32.5 metres. However, the view to the east into the choir does not show the original picture of the 12th century, because when the original choir was completed in 1182, there was no tracery yet. The interior also underwent radical changes between its first and final completion. In the beginning it did not even have a vault.
The nave originally had a four-storey wall plan with triforium as in the cathedrals of Noyon and Laon. However, as the interior was too dark with the arcades only beginning at a great height, this was changed from 1220 to a three-storey wall construction with a tracery storey in the clerestory, following the example of Reims.
In one place - around the crossing - Viollet-le-Duc reversed the change in the 19th century in order to document the original state at least here. What appears to be a breach of style in the building's present form can thus be explained by the monument preservation intentions that began at that time, which had not existed in the centuries before.
Retaining Romanesque forms, the columns delimiting the nave have a round cross-section and end in capitals under the arches of the side aisles. In Gothic style, however, the services on top of them lead up to the vaults of the nave.
The nave and transept, at 32 metres, are considerably higher than the side aisles, and at over 12 metres are about twice as wide. In order to give each bay an approximately square aspect ratio on the one hand, and on the other hand to lead all services to the apex, one nave bay corresponds longitudinally to two side aisle bays, is supported on six columns and has six bays. The inner aisles of the transepts separating the side aisles from the choir ambulatories and the front two nave aisles of the choir are designed in the same way. The last nave bay of the choir with the polygonal apse has eight fields. The vault of the crossing has, of course, only four bays, as do the outer bays of the transepts, which deviate strongly from the square ground plan and were only built in the extension phase.
In the rows of columns separating the inner and outer aisles, every second column is more Gothic in design, and almost the entire shaft is surrounded by services.
Transept
The floor plan shows the unusual shape of the choir of Notre-Dame. The ambulatory and chapel chapels actually merely continue the side aisles of the nave and encircle the choir with mathematical precision. In 1330 the choir chapels were added, so that the cathedral appeared as if it had seven naves, and the transept in the middle hardly stood out.
In order to allow the transept to project beyond the alignment of the chapel walls, the old transept façade had already been demolished in 1267 and this part of the building extended by a bay on both sides and provided with a new façade, which was now so ornate and elaborately designed that it no longer threatened to be lost in the rest of the building. The new, huge windows are of the finest tracery. They are among the best and most beautiful in the field.
The style level of tracery windows is called "rayonnant" in art history, i.e. radiating. From 1270 to 1380, the tracery style prevailed in France (High Gothic). The transept façade of Notre-Dame in Paris is also one of the first and most important of this style.
Reflections
To begin the construction of churches with the chancel and to consecrate it, that is, to give it its function, long before the other parts were completed, was the usual procedure at a time when worship was understood primarily as the service of priests to God. Some churches from the Middle Ages still consist only of what was once supposed to be the choir. But that the modernization of older parts was begun scarcely after the original plan had been more or less fully executed is probably seldom so evident as in the case of the Cathedral of Notre-Dame in Paris.
The Gothic architectural style developed in the environment of the French royal court. Nevertheless, it is not surprising that the cathedral of the capital was not the first great Gothic church, but the abbey church of Saint-Denis. Paris was not yet the pre-eminent metropolis of the country. The abbey church, as the burial-place of kings, held a pre-eminent position among the places of worship of the kingdom. France was not yet ruled absolutistically as under Louis XIV. Apart from royal benefactors, the builders of the great churches were high church officials. It depended to a large extent on their ambitions when and where architectural innovations were introduced. Among these powerful churchmen were Suger of Saint-Denis, abbot 1122-1151, and Maurice de Sully, bishop of Paris 1160-1196.