With two more men convicted on Sunday for joining ISIS, there are now nine French nationals on death row.
Fodil Tahar Aouidate and Vianney Ouraghi were among 11 French citizens and one Tunisian handed over to Iraqi authorities in January by a US-backed force fighting the jihadist group in Syria
Described as violent and ready to die for the extremist ISIS ideology, Aouidate first appeared in court on May 27 but a judge delayed his trial and ordered a medical examination after the 32-year-old claimed he was tortured into confessing.
"The medical report shows that there are no signs of torture on his body," the judge told the court before handing down his sentence.
His trial was quickly followed by that of 28-year-old Ouraghi, who acknowledged in court that he "worked with" ISIS but said he did not participate in any fighting.
Baghdad has handed capital punishments to seven of the other French jihadists and the Tunisian over the past week.
Hearings for the last two suspected French ISIS members to be tried in Baghdad are set for Monday.
Iraq has sentenced more than 500 suspected foreign members of ISIS since the start of 2018.
Its courts have condemned many to life in prison and others to death, although no foreign ISIS members have yet been executed.
Those convicted have 30 days to appeal.
Ouraghi, who has Algerian roots, left France for Syria in 2013 and joined the Al Qaeda affiliate there before jumping to ISIS when the latter declared its "caliphate" in 2014.
"Yes, I worked with ISIS, but I did not participate in any combat in Syria or Iraq," Ouraghi said in classical Arabic, which he picked up in Egypt.
Sporting thick glasses and a light brown goatee, he pleaded that he was only an "ISIS administrative officer" in charge of "widows and families" of the jihadist group.
Aouidate showed no reaction when the judge handed down his death sentence.
He first went to Syria in 2013 and returned in 2014 with 22 members of his family to join ISIS, according to the French judiciary.
Authorities also linked him to Belgium's Salafist movement including Abdelhamid Abaaoud, the suspected mastermind of the 2015 Paris attacks.
Interrogated for four months, he alleged during his first hearing that he was beaten to "confess" to the charges levelled against him.
Human Rights Watch on Friday accused Iraqi interrogators of "using a range of torture techniques... which would not leave lasting marks on the person's body".
It also condemned France's "outsourcing" of trials of ISIS suspects to "abusive justice systems" and criticised Iraq's "routine failure... to credibly investigate torture allegations".
France has long insisted its adult citizens captured in Iraq or Syria must face trial before local courts, while stressing its opposition to capital punishment.
The death penalty was abolished in France in 1981 and French law forbids the government extraditing someone who could face the death penalty for their crimes without specific guarantees that the sentence will not be handed down. But the nationals handed over to Iraq are not covered by this as they were not deported from France.
French government spokeswoman Sibeth Ndiaye reiterated on Sunday that officials were intervening "at the highest level" in the cases.
"France's position has been constant... As soon as our citizens around the world face the possibility of a death sentence after a conviction, we intervene at the highest level of state," Ms Ndiaye told Europe 1 television.
Iraqi law provides for the death penalty for anyone joining a "terrorist group" – even those who did not take up arms.
*Additional reporting by AFP
