Interestingly enough, it defines web host as "the natural or legal persons that provide, even gratuitously, for provision of public services to the public online communication, storage signals, writings, images, sounds or messages of any kind provided by recipients of these services. ". It doesn't come right out and say, but it looks like if you allow the creation of online content, or the sharing of such content from within France, you need to keep this information.
Application of article 6 II of the LCEN
Enforcement Decree of the LCEN on data retention by ISPs and hosters "Digital Crime
The following is the Google Translation from here.