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In what could be the first report of an attack by Islamic State militants on French special forces using a drone, the device was intercepted while flying and exploded after landing on the ground, the paper said.
Le Monde said the attack happened on Oct 2.
It was not clear whether the device was remotely detonated or if it carried a timed bomb.
The two French soldiers were immediately repatriated to receive medical treatment in France. One of them "is between life and death," Le Monde wrote.
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Other French soldiers were also lightly wounded by the explosion but Le Monde did not give precise numbers.
France has about 500 military in Iraq as part of a US-led coalition to fight Islamic State militants.
The numbers include special forces that have been training Kurdish Peshmerga forces in the north of the country.
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The French defense ministry, which has a policy of not discussing special forces' operations, declined to comment on the Le Monde report.
An Iraqi military spokesman in Baghdad could not confirm the report and Peshmerga sources were not immediately available for comment.
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