The six have been charged with recruiting would-be jihadists to fight in Syria and raising funds for armed Islamist groups fighting there, legal sources said Friday.
One of the men, who are aged between 32 and 38, has been identified as the network’s leader.
Four of the group have political refugee status, one has Russian and French double nationality and the fifth obtained French citizenship in 2009.
They were rounded up last weekend in or near the south-western cities of Toulouse and Albi.
On Thursday French Prime Minister Manuel Valls expressed concern at the “particularly worrying” influence of Islamist groups in the “Chechen movement”.
Chechnya is a Muslim-majority autonomous republic in the Russian federation that has been through several separatist revolts.
About 1,400 French citizens or residents are in contact with networks sending fighters to Iraq and Syria, where the Islamic State armed group controls a swathe of territory.