The Al-Qaeda linked Shebab said in a statement they have "reached a unanimous decision to execute the French intelligence officer, Denis Allex," who goes by a pseudonym.
On Saturday, French commandos launched a raid to free the hostage, but the rescue bid failed and resulted in the death of two French soldiers.
French officials suggested at the time that Allex was most likely killed in the raid, a position echoed by the governor of the lower Shabelle region where the raid took place.
But Al-Shabab spokesman Ali Mohamud Rageh told a news conference on the phone that Denis was still alive.
Wednesday’s statement did not explicitly say whether Allex was still alive.
The French army responded to the statement by accusing the Shebab of "manipulating the media", and reaffirmed that Allex is likely already dead.
France's Chief of Defence Staff Admiral Edouard Guillaud told Europe 1 radio: "We have no element since the raid indicating Denis Allex is alive. We think he is most likely dead," he said.
French Defence Minister Jean-Yves Le Drian said Saturday that the raid, by the elite DGSE secret service, was sparked by the "intransigence of the terrorists who have refused to negotiate for three and a half years and were holding Denis Allex in inhuman conditions."
The minister said at the weekend that a French soldier was missing, but on Monday he said it now appeared that the soldier had died. He did not indicate that he was a commander. Le Drian said 17 guerrillas were killed in the raid.
Sources in Somalia said one of the reasons the raid failed was that the rebels had received advance warning, which senior Shebab commander Sheikh Mohamed Ibrahim confirmed to the news agency AFP.
Le Drian's explanation was that French troops had underestimated the Islamist rebels' strength when they launched the operation involving some 50 troops and at least five helicopters, and some help from the United States.
President Barack Obama has acknowledged that US forces provided limited technical support for the operation, but said they had played no role in the fighting.
Denis Allex is the longest held French hostage overseas since French-Colombian Ingrid Betancourt, who had been held for more than six years by Colombian guerrillas until being rescued by Colombia's security forces in