The six were arrested in a dawn raid in Strasbourg, the capital of the eastern region of Alsace and seat of the European parliament.
The operation “went perfectly”, according to Interior Minister Bernard Cazeneuve.
"It's a new demonstration of the government's complete determination to do everything in its power to fight terrorism and the indoctrination of young people," he said. "The plan to fight jihadi cells, as presented during the cabinet meeting of 23 April, is therefore being applied in a determined way, without weaknesses."
Two young men from the area where the raid took place have been killed in Syria and several others returned about a month ago, according to local people.
They were part of a group of 15 who told their parents they were going on holiday in Dubai and, with the exception of one who was stopped by his parents, in fact took a plane for Turkey, going on to a jihadi training camp and then to the combat zone, Europe 1 TV reports.
They were all of north African or Turkish origin and had not previously been close to radical Islamism but seem to have been recruited quickly via social networks and contacts in France.
The government recently reorganised anti-terror police and launched a website and phone service for parents fearing that their children were thinking of enrolling in armed groups abroad as part of an anti-jihadi campaign.