In the video posted online on YouTube on Tuesday, nearly a month after Islamist attacks in Paris, an unidentified, masked jihadist is seen surrounded by militants calling on French Muslims to quit their country for IS' self-proclaimed "caliphate", which covers parts of Iraq and Syria.
President Francois Hollande is referred to as "the doormat of the Jews" and French Muslim leaders Hassen Chalghoumi and Dalil Boubakeur are called "leaders of hypocrisy".
Boubakeur, the rector of Paris's mosque and Chalghoumi, the imam of the Drancy mosque in the northern suburbs of Paris, are known for their strong opposition to fundamentalists.
"Your blood will continue to flow," the jihadist threatened in the video.
The preliminary investigation, assigned to France's national intelligence agency, is based on grounds of provocation to conduct terrorist acts using online communication services, possession of weapons, and death threats connected to a terrorist organisation.
The video shows seven jihadists with masked faces and armed with Kalashnikovs, including what seems to be a veiled woman revealing only her eyes.
CNN identified her as Hayat Boumeddiene, the partner of Amedy Coulibaly, one of the three gunmen behind the Paris attacks.
But a source close to the investigation told AFP: "There is no certainty that is her."
Boumeddiene is said to have left France for Syria via Turkey in the beginning of January, days before the Paris attacks.
The jihadist who speaks in French also pays tribute to the perpetrators of the attacks that left 17 dead.
He asks supporters to attack police and military targets, as well as those who participated in mass protests last month to condemn the killing of 12 people at the offices of French satirical magazine Charlie Hebdo on January 7th.