Is it possible to study French as a foreign language at a French university?
Yes, but they want you to have at least two years of study before applying. They do not teach classes to beginners. Well, they do but it will just be a summer class, they would not teach beginning French to you are a whole year, you would just be taking one class because they don’t teach any other classes in English. You will not end up with qualifications for anything, just a knowledge of French; which will not get you anywhere. But if you already speak French well enough to pass the language proficiency exam you can study anything that you want there. France is a very strong country culturally, so you are not going to be able to attend University without being able to speak French unless you are attending an America University there, and there are a couple.