Confirming a report in Le Monde newspaper on Saturday, the source said the men aged 23 to 25, who were arrested in the eastern French city on Tuesday, were under investigation for criminal conspiracy in relation with a terrorist undertaking.
They were suspected of traveling to Syria late last year to join the foreign-hatched conflict against the Syrian government.
European governments calculate several thousand of their citizens have gone to Syria since the war began three years ago and are worried about the security risk posed by youths radicalized by the conflict.
France, which estimates around 285 of its citizens are currently fighting in Syria among the militants' ranks, last month launched a plan to prevent its citizens joining the war and becoming a threat to their home country.
Under the new policies, French nationals who return from Syria could face charges of being part of a terrorist organization, while minors could be prevented from leaving France without parental consent.
It also launched a hotline for parents concerned about their children's behavior.
Syria has been gripped by deadly unrest since 2011. According to reports, Western powers and their regional allies - especially Qatar, Saudi Arabia, and Turkey - are supporting the militants operating inside the country.
NTJ/HH