I'm no expert, and razors could be bought with the name of the retailer, just like many another thing in those days, but there most certainly were numerous French razors of high quality. Here is the link to the Coupe-chou Club. It is entirely in French, but even if you don't speak it, you can do a search, and any translation website will tell you enough to know if you have a French razor.
Coupe-Chou Club
There seem to be psychological reasons for many people to have a deep suspicion of French engineering operations in general. But in a good many areas of technology, the facts do not bear this out. They seem to have a great flair for ergonomics, and what could be more relevant to the straight razor than that?
Google Maps can be a big help. Angers and St. Aignan are towns in France, "fils" means Son, and "No." meaning Number, with the o in superscript, might be in Spanish or Italian, but is more likely to be French, and not German or English. Two initials back to back is often found in French, and F as the second letter could easily be "frères", meaning brothers. As the second it could be "Français" for French, or "Fabrique" for factory. Manufrance, for example, was the Manufacture Française des Armes et Cycles de St. Etienne, so FF could easily be Fabrique Française de Something Else.