Bonjour,
Near Menton, the only airfield where you may teach as FI is Cannes (68km from Menton approx 1h)
Most of the flying clubs in France don't pay their FIs even if they ask students to pay for it... (Less than 10% FI in France are paid, others are "volunteers")
And they will probably ask you to pay a year subscription fee and some hours with a FI even if you have lot of time on the aircraft.
Up to you.