The fate of the hostage, Denis Allex, was unclear, Radio France International reported Saturday.
In reporting the overnight Friday raid, French Defense Minister Jean-Yves Le Drian said Allex was killed by his captors. Al-Shabaab said the hostage was alive, but had been moved to a new location and his fate would be decided within the next two days.
Allex has been held in what France said was inhumane conditions since his capture in Mogadishu in July 2009.
Soldiers in four helicopter gunships raided the southern Somali town of Bulomarer where Allex was being held, witnesses said.
Afterward, they reported seeing a number of bodies, including that of a white man.
A French soldier was killed in the rescue mission, but his body was left behind after two attempts to retrieve the remains failed, a resident said.
A second soldier was missing, Le Drian told reporters in Paris, the BBC reported.
Al-Shabaab, in a statement, said the "fierce firelight" had lasted 45 minutes.
The insurgents said a wounded soldier left behind was now "in the custody of the mujahideen," CNN reported.