A Baghdad court on Monday sentenced another former French fighter with the ISIS group to death - the fourth Frenchman to get the capital punishment so far in Iraq - and postponed the verdict for a fifth man after he testified to being tortured in detention.
France, meanwhile, said the Iraqi court has jurisdiction to rule in the cases, though a spokeswoman reiterated the French government's opposition to the death penalty.
The trials come as questions swirl about the legal treatment of thousands of foreign nationals formerly with the extremist group.
The Frenchmen on trial are among 12 French ISIS fighters whom the US-backed Syrian Democratic Forces handed over to Iraq in January. The Kurdish-led group spearheaded the fight against ISIS in Syria and has handed over to Iraq hundreds of suspected ISIS members in recent months.
ISIS "terrorists must answer for their crimes in court," said France's foreign affair's ministry spokeswoman, Agnès von der Mühll.
As Monday's proceedings opened, the first to appear was Mustafa Mohammed Ibrahim, 37, from the Mediterranean city of Nice. Ibrahim, of Tunisian origin, with short hair and a light beard, walked in the courtroom wearing a yellow prison uniform with "Reforms Department" printed on the back in Arabic.
"I ask for forgiveness from the people of Iraq and Syria and the victims," Ibrahim said before Judge Ahmed Mohammed ordered he remove his top in order to see if there were any signs of torture on his body. None were visible.
"No matter what the sentence will be against me I want to go back to my country," said Ibrahim. He added that he used to work as a driver back in France before joining ISIS.
The judge sentenced Ibrahim to death.
The second man brought into the courtroom was identified as Fadil Hamad Abdallah, 33, of Moroccan origin. Abdallah said he was subjected to torture while in detention and the judge referred to him to a medical committee for investigation and postponed his next session until Sunday. The judge also postponed the sentencing of three other Frenchmen until next Monday.
The first three French ISIS fighters were sentenced to death on Sunday. Those convicted can appeal their sentences within a month.
Iraqi prosecutors say the 12 French nationals were parties or accomplices to ISIS crimes, and threatened the national security of Iraq. Simply belonging to the extremist group is punishable by life in prison or execution under Iraq's counter-terrorism laws.
In Paris, von der Mühll said France's position is that adults detained in Iraq must be tried by the Iraqi justice system, as soon as it declares itself competent.
"France respects the sovereignty of Iraqi authorities" she added, though she expressed her country's opposition to the death penalty, "in principle, at all times and in all places."