Armed officers made the arrests in early morning raids in the eastern city of Strasbourg.
Minister Bernard Cazeneuve said the raid demonstrated "the government's absolute determination to fight with all its force against terrorism and the indoctrination of young people".
Cazeneuve said earlier this month that 285 French extremist citizens were currently fighting in Syria, despite a slew of measures to prevent people from travelling to the war-torn country.
There have been mounting concerns in France over the number of young militant heading to fight in Syria, with authorities fearing they could pose a major security threat if they return home as battle-hardened veterans.
The French government unveiled an anti-terrorism plan in April to prevent the radicalization of nationals, thwart online recruitment and make it more difficult for aspiring militants to leave the country for Syria.
Europe1 radio said 14 would-be militants had travelled to Syria from Strasbourg after telling their families they were going to Dubai on holiday.
Media reports says the men were recruited via social media channels.
NJF/NJF