Using the pseudonym "Abou Salman al Faransi", 26-year-old Othman Garrido is believed to have arrived in the region in 2012, where anti-terror prosecutors (PNAT) say he committed "murder in connection with a terrorist undertaking" and joined a "terrorist conspiracy".
He is believed to have played an important role in and have information on the .
A judge on Friday ordered him jailed provisionally after he spent the week in police custody.
"Based on photographs of abuses where he is visible", Garrido "was likely involved in other murders in Iraq and Syria" being probed in a separate investigation, PNAT said.
Prosecutors suspect him of three murders in total, although they have not been able to precisely date the crimes.
France has had an arrest warrant out since 2016 for Garrido, a native of southern city Montpellier.
Turkish forces captured him near the Syrian border in July, and handed him over under a Paris-Ankara deal covering the return of French jihadists.
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A youth court sentenced Garrido in 2017 to 15 years in jail for joining the Islamic State (IS) group in Syria, where he trained and fought as well as attempting to incite violence by French Muslims.
After burning his French passport, Garrido urged Muslims to kill "infidels" in a seven-minute video distributed by IS' communications arm in 2014.
He was flanked in that recording by two other French jihadists using the pseudonyms Abou Ousama al Faransi and Abou Maryam al Faransi.
Garrido's parents and two of his brothers have also received jailed sentences of 10 and 15 years.
It is unclear whether his brothers, who also travelled to Syria, remain alive.
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