Although he was also a prolific writer and historian, Abbot Suger is arguably most famous for his contribution to the reconstruction of Saint-Denis in the middle of the twelfth century. With its adoption of new architectural styles and forms (the church has the first known example of a large "rose window" above the West portal, for instance), Saint-Denis is often cited as the first example of Gothic architecture and the cathedral that inspired the construction of countless others in France in the years to follow.

Although there are other French churches or cathedrals in this list of answers, the only one that is part of the Gothic architectural movement is the Notre Dame. In fact, the only answer, French or otherwise, on this list that is truly a Gothic cathedral is the Notre Dame cathedral.

This cathedral, known as the Reims Cathedral, was built in France in the year 1211.  It very accurately depicts the popular architectural trends that were popular in that time period, which is now known as the Gothic period. This period took place between the 12th and 16th centuries. Features popular in Gothic architecture that can also be seen on this cathedral are:

1) Vertical length over horizontal length.  Gothic buildings tended to be slender and tall.

2) Pointed arches

3) Spires and towers, especially when they come in doubles.

4) Ornate façades

5) Rose windows

Image citation: Photo taken by bodoklecksel (2006) https://upload.wikimedia.org/wikipedia/commons/e/e1/Reims_Kathedrale.jpg

The Chartres Cathedral of the early 13th century is an example of Gothic architecture. Its Gothic features are the following:

1) Vertical length over horizontal length.  Gothic buildings tended to be slender and tall.

2) Pointed arches

3) Spires and towers

4) Ornate façade (though not as ornate or decorated as other Gothic buildings)

5) Rose window

6) Groups of large windows

Image citation: Photograph taken by Tony Hisgett, accessed through Wikipedia Commons. https://commons.wikimedia.org/wiki/File:Chartres_Cathedral.jpg

Gothic architecture dominated between the fall of Rome in the fifth century CE and the rise of the Renaissance in the fifteenth century. Gothic architecture was notable for large, ornate stone structures with many elements and imposing figures. All of these are best seen in the many Gothic cathedrals that allowed architects and designers their most control over the shape of buildings.

A key feautre of Gothic churches is their extreme height. This verticality was partly for show, but more importantly symbolized an attempt to reach heaven. For many centuries, Gothic cathedrals were the tallest buildings in Europe.

Three is perhaps the most powerful number in the Catholic world, representing the holy trinity. Gothic cathedrals often featured three doors- a center door as well as two flanking doors. It was believed that one walked in the door a sinner (these were the flanking doors) and walked back out through the grand center doors absolved of their sins in the eyes of God. 

The centermost sweeping area of the church is the nave. Its length is what contributes to the rectangular nature of the plan. The aisles are what give the church its cross shape, and the transepts are the outcroppings on the sides. The apex is the half-circle at the top of the nave across from the doors, and is where the church official would stand. 

The gothic cathedral in general was a display of grand architecture and ornate visual elements, and the church was dominant over the state at that time. But the best answer is the Catholic church's tradition and value in Gothic society. The churches were not meant to impose dominance over secular law, at least not directly; what they were meant to do is reach towards the heavens, encompass the Catholic's desire to be close to God and to build a holy space as grand as one could.