This is French national Denis Allex as he appeared in an undated video released by Somali militants.
Al Shabaab rebels linked to al Qaeda said on Thursday they had executed Allex, who French armed forces had tried to rescue over the weekend.
The militant group said on its Twitter account that he had been killed at 1630 GMT on Wednesday.
This has not been confirmed by other sources as the news spread on Thursday.
The militants said the decision to kill Allex was unanimous and followed three years of what it called exhaustive attempts at negotiation.
France, however, said it believes the Frenchman was killed in Saturday's failed rescue mission, and has accused the militants of manipulating the media.
In the video Allex is seen pleading for his life.
(SOUNDBITE) (French) FRENCH HOSTAGE DENIS ALLEX READING FROM SHEETS OF PAPER, SAYING:
"Mr. President, I am still alive, but for how long? That depends upon you, for if you do not reach an agreement for my release, then I am afraid this will be the last message you receive from me. My life depends on you."
Allex was one of two French intelligence officers who were kidnapped in Mogadishu in July 2009, though the other man escaped a month later.
Two French commandos were killed in Saturday's failed rescue attempt.
Somali militants say execute French hostage (1:30)
Jan. 17 - Somali al Shabaab militants say they have executed a French hostage who French commandos tried to rescue at the weekend. Travis Brecher reports. ( Transcript )