Residential rentals in France fall into two categories that basically split according to whether the flat is furnished or not. Furnished properties are governed by the rules for holiday rentals and hotels, whereas unfurnished have their own statute with lots of protections for the renter (i.e. to avoid the evil landlord tossing a family out into the snow in the dead of winter).
Furnished rentals can be limited to particular seasons, either because the property isn't equipped for the off season (e.g. not properly heated for winter occupation) or because the landlord charges a considerably higher rent (often weekly) for the peak season. Unfurnished rentals rent on a 3-year lease term (with specific terms and procedures for terminating the lease in the interim). It kind of depends how you are planning on scheduling your time in France and whether you want to rent something "full time" or if you're ok with completely moving out and moving back in with each visit to France.
But 3-year leases can be very difficult for newcomers to France. Most landlords expect to see three months of back pay slips (usually only French payslips) and evidence that your regular income is deposited into a local account each month. There is no central credit rating agency in France and your US credit history means nothing over here, so you sometimes have to get creative.
Cheers,
Bev