AFNIC is the registry for domain names in .fr and all French extensions. It is in charge of first level domains (ccTLD) for France (.FR), Réunion (.RE), Saint Pierre and Miquelon (.PM), the French Southern and Antarctic Lands (.YT), Mayotte and Wallis and Futuna (.WF).
Youdot is an authorized registrar with more than 20 registries, including AFNIC.