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Police provided no further information about the arrests but Interior Minister Manuel Valls said they were linked to the capture of an individual on the Mali-Niger border several months ago.
The probe is being conducted by French intelligence agents, a police source said, adding that several dozen French nationals had travelled to Syria to fight in the conflict there, sometimes in groups linked to Al-Qaeda.
There are also people who want to go to west Africa, where the French army last month deployed to fight Islamists occupying the north of Mali, he said.
A "handful" of French would-be jihadists are probably already in Mali, he said.
French forces intervened in Mali last month to halt an advance on the capital Bamako by Islamists who seized a swathe of the north in 2012.
With the Malian army, the French have taken back large chunks of territory from the militant groups, but concerns remain that the fighters have simply gone underground.