Rich as compared to what? French cuisine is one of the world's great cuisines, but how do you compare "richness"? And what does tradition mean in this context? History, or contemporary practice inflected by history?

One might more easily ask what caused French cuisine to become a prominent world cuisine. There are many factors. Perhaps the most significant is the major wave of French cookbook publishing in the 17th and 18th centuries coinciding with the European predominance of French culture--when the courts of Europe spoke French. This both created a national cuisine and diffused it across Europe. It established the backdrop for the creation of multiple culinary institutions and practices. The French invented the restaurant in the 1780s. One might also look at French celebrity chefs at various European courts, such as Antoine Carême in the early 19th century working for Talleyrand, George IV, Alexander I, etc. In the same period the French created gastronomic writing--Grimod de La Reynière and Brillat-Savarin. This heritage was consolidated through the 19th century and into the 20th century by the creation of teaching and critical institutions like the Cordon Bleu and the Guide Michelin.

Pascal Ory, Le discours gastronomique français, des origines à nos jours (Paris, 1999)

Food : a culinary history from antiquity to the present, Flandrin and Massimo Montanari , eds., (NY, 1999)

Jean Louis Flandrin, Arranging the Meal, (Berkeley, 2007)