Interior Minister Bernard Cazeneuve said there is a "strong presumption" that Maxime Hauchard is among the group of Islamic extremist fighters in the video released over the weekend. He urged young people in France to "open your eyes to the terrible reality" of the militant group.
Cazeneuve said authorities were analysing the video and have been investigating Hauchard, who is around 22 years old and from west of Paris. The convert to Islam gave an interview to France's BFM television in July, telling the network he had helped in the capture of Mosul, the Iraqi city whose fall eventually prompted the United States to resume military operations there.
French citizens make up the largest contingent of European jihadi fighters who have joined extremists in Syria and Iraq. According to the Paris prosecutor's office, about 1,100 people have been placed under surveillance, and 95 people face charges.
Hauchard, who is believed to have arrived in Syria in 2013, is among those under judicial investigation, Cazeneuve said.
"From a personal point of view, my objective is to be a martyr," Hauchard said.