Police said the raids were conducted in several cities as part of an ongoing operation that began after gunman Mohamed Merah killed seven people in the Toulouse area last month, Le Figaro reported.
Police conducted similar sweeps last week.
Officials said Wednesday's operation had no direct tie to the Merah case. Police said the people arrested, including so-called lone wolves who are not part of a network, are suspected of planning Islamic violence. They allegedly had been to militant training camps in the Afghanistan-Pakistan region.
France's domestic intelligence agency led the raids, police sources said.
Citing police sources, Radio France Internationale reported two men and a woman were arrested in Roubaix and 10 others were detained in Marseille, Carpentras, Valence and Pau and in the Lot-et-Garonne department.