90% of the French Flying Clubs are members of the FFA (French Powered Aircraft Association) ( in French "membre affilié à la FFA").
Each member of a "aéro-club affilié" must compulsory subscribe a membership to the FFA.
No further difficulty. You enter a flying club house, you file right away a subcription form, you pay, and you become a FFA member.... In the same time, you do the same for the local aéro-club membership...
In this FFA membership, a part is for the FFA runing costs (eg: the FFA gives a little money for youngsters who get their PPL's, ...), the rest is for your personal insurance (in French: "assurance individuelle") when practising powered aircraft.
Don't pay an extra charge for the monthly FFA magazine: 1. you can't read French, 2. Brit mags are far better, 3. What you will read in this mag is still on different internet sites.
The FFA membership is only annual, valid from the subscription date till the 31th December of the current year, valid everywhere in France.
Another point: I'm afraid 'hiring' is not a suitable word. A "aéro-club" is not a commercial business, although some big clubs are running as commercial bodies. It's a non-profit association, it's not a Rent-a-Plane body.
A aéro-club member is a aircraft part-owner like one in a flying group, he takes part to the flying activity by using (not hiring) aircraft. He has no rights but duties.
French people go to different associations because they're VAT exempted and therefore are cheaper, but still acting as demanding customers...
WW, old-fashioned pilot, since 1964.