If you have an EU driving licence you can drive in France even if you are a resident. But if your licence isn't EU you'll have to get a French "permis". In some cases - where France has a reciprocal arrangement with your home country or state - this is simply a matter of exchanging your old licence for a new French one.

Does your licence qualify for an exchange? Check the list at: http://trim.li/nk/licence
If yes, don't bother with all the forms and details online. Just go to the Prefecture and ask to exchange your licence. Once they verify you are eligible, they'll give you an archaic piece of paper (not possible to download) called “Demande de conversion de permis de conduire etranger”. Go home. You'll need to fill this in and post it with:
1/Photocopy of both sides of your driver's licence
2/ Photocopy of both sides of carte de séjour or nationality card (EU citizens).
Enclosing a photocopy of an official translation of the licence doesn't hurt. Send this (lettre recommandée always a safe bet) to:
Prefecture des Alpes-Maritimes
Bureau de la circulation
Permis de conduire 06286 Nice Cedex 3.
After 2 months or so and you'll receive a convocation letter asking you to go to the Prefecture between 9-12 with:
1/ 2 identical ID photos
2/ Original drivers licence;
3/ Self addressed stamped envelop (up to 20g)
4/ Their enclosed form filled out and signed (similar to CERFA N° 11247*02).
Also a good idea to submit photocopies of carte de séjour or passport and official translation of licence.
Tip: Be sure that the type of licence corresponds to B (car) on the French permit.
You'll was given a piece of paper (a temporary licence “Certificat valable 2 mois”) and told your licence should arrive by post within three weeks.