The six who were known to police for being radicalized were arrested as they planned to travel to Syria, according to reports in the French press.
Some had openly declared their allegiance to the terror group Isis, while others were known to police for calling on people to join jihad.
The five men and one woman were all from the Lyon region and have been placed in police detention to be questioned on suspicion of terrorism offences.
According to BFM TV, certain members of the group had been trying to procure arms with the intention to attack swingers clubs.
No further details of when, where or indeed how the suspects had planned to carry out the alleged planned attack have been revealed.
According to reports, no arms were actually found during searches of their homes, which were ongoing on Tuesday morning.
The six had bought bus tickets to travel to Syria via Bulgaria and Turkey, but French counter-terrorism police decided to intervene before they left.
The news comes as France remains on edge and under a national state of emergency after terrorists killed 130 people in shootings around Paris in November.