The al Qaeda-linked group also claimed the hostage, Denis Allex, is still alive, and that they would soon display the bodies of the two commandos.
The militants put up fierce resistance when French special forces went into southern Somalia by helicopter on Saturday to try to free Mr Allex.
There was confusion over the mission's outcome, with France initially stating one soldier and Mr Allex had been killed, and the other commando was missing.
Mr Allex was one of two officers from France's DGCE intelligence agency kidnapped by al Shabaab three-and-a-half years ago. His colleague escaped a month later.