Excellent topic! I've been giving this some thought as well. I can see three main reasons.
One is that Louis XIV and his minister of finance Colbert deliberately put in place a policy to make France the main purveyor of luxury goods, and to make Paris the hub of fashion for Europe. From that moment, the combination of high-end luxury or trendy goods made in France, and of the prestige they acquired through "marketing", made France the place to turn to for the best, most fashionable items, including perfume and cosmetics.
The other is that the town of Grasse benefitted from this policy, as well as from its ideal micro-climate, to develop the art -- if there is a constant demand for newer and more refined products, there will be more creativity and technical advances.
The third reason is the prestige acquired by Paris couture in the early 20th century: at the time, perfume wasn't the couturier's cash cow (they actually made their money with their clothes) and they could afford to experiment, be creative with their perfumers, thus creating several of the templates of modern perfumery.
Probably also the genius of people like François Coty, who pretty much pulled the whole industry into the 20th century, was also a factor.
Perfume could have been Italian (it was up to the 16th century), and it could have been English (London was a competing perfumery center in the 19th). Despite the fact that there are major perfume houses/brands in other countries today, "perfume" and "French" are still durably associated and French perfumers are all over the labs in every country... The latter phenomenon is probably also due to the fact that up to recently (the founding of the perfumery school in Versailles, ISIPCA), one of the few ways to break into the industry was growing up in Grasse and being part of a dynasty.
I'm sure there are other reasons and I'm looking forward to reading them!