The official, who spoke on condition of anonymity in line with regulations, said the two are Murad Mohammed Mustafa , 41, and Bilal Abdel-Fattah, 32.
They are among 12 French IS members who were arrested by the U.S.-backed Kurdish-led Syrian Democratic Forces and transferred from Syria to Iraqi custody in January.
None of the death sentences have yet been carried out, but France is intensifying diplomatic efforts to spare its citizens from execution.
Abdel-Fattah and Mustafa are the final French nationals to be tried in Iraq. The other 10 have all received death sentences.