The move comes after three days of police questioning of the five after security forces detained them in connection with the network in southern Lunel. Authorities yesterday said at least six people from the town died in Iraq and Syria in recent months.
Interior Minister Bernard Cazeneuve has said Tuesday's raids dismantled a jihadi network.
France says about 3,000 citizens have links to extremist fighters in Syria and Iraq, with important contingents in both the Islamic State group and al-Qaida-linked Nusra Front.