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Information on domestic flights in France is not easy to come by, one reason being that Air France has such a dominant position in France and already have flights on most internal routes.
Plus the French market is not as competitive. The French Railway system between major cities is both fast and competitive, especially if starting from Paris.
I have only been able to uncover a couple of airlines which offer domestic flights in France:-
http://www.easyjet.com/ - Toulouse to Lyon, Paris, Nice to Paris; Lyon to Biarritz, Bordeaux; Biarritz to Paris

http://www.twinjet.net/
Toulouse (32 Haute-Garonne, Midi-Pyrenees) to Metz/Nancy, Mulhouse, Brest; Marseille to Metz/Nancy, Mulhouse; Paris - Perigueux, Cherbourg

http://www.airlinair.fr/ Brest,(29 Finistere, Brittany) Bordeaux (33 Gironde, Aquitaine), Agen (47 Lot-et-Garonne, Aquitaine), Lyon (69 Rhone, Rhone-Alpes), Poitiers (86 Vienne, Poitou-Charentes), Brive (19 Correze, Limousin) Beziers (34 Herault, Languedoc-Roussillon) etc

http://www.ryanair.com/ now also has links from Marseille (13 Bouches-du-Rhone, Provence) to Lille (59 Nord, Nord-Pas de Calais) and Brest (29 Finistere, Brittany)

You can try sites like http://www.expedia.fr/ but even a price comparison site like http://www.baisse-de-prix.com/voyages.php seems to offer little new – it looks like Air France have cornered the market with little opportunity for discounting.