The other nine French citizens were reportedly convicted between May 26 and June 2.
"An Iraqi court has issued a death sentence to two Frenchmen for joining the Islamic State" the source told the broadcaster.
One Tunisian national was also sentenced to death over the given period, the broadcaster added, citing the source.
The foreigners are believed to be part of a group of around 280 suspected Daesh militants, including at least 11 French citizens, who were transferred from Syria to Iraq by the US-backed Syrian Democratic Forces a few months back, according to Human Rights Watch.
The rights group reported last week that at least two of the convicted French nationals had told the court that they had been tortured while in detention and coerced into confessing, with the judge showing little interest in verifying their claims.
*Daesh (also known as ISIS/ISIL/IS) is a terrorist group banned in Russia