All you have to do is read everything written in the link...
Each country delegates the issuance of International Driving Permits to an approved office. Sometimes it’s an automobile association, but not always. In France, it’s the ANTS that was chosen.
If you want, you can request that it be delegated to the FNAC, but I’m afraid one part of the process might bother you...
There’s a verification of the validity of the driver’s license you submit against the database of said licenses...