Most private flying in France is through aeroclubs. The joining fee
("cotisation") is required for insurance reasons and maybe tax
regulations (I don't know nor care about the details). You'll have to
pay that "cotisation" in every club.

Commercial FBOs as in the USA don't exist in France. The only way to
"just rent" a plane would be to find a fully commercial flight school.
Those are very rare in France. Your best bet would be to contact some
clubs and just ask them. They may or may not know such a school.

Stefan