Mr Allex - a French spy - was kidnapped in Somalia in July 2009.
BBC: Denis Allex: French agent 'killed' by Somalia al-Shabab
French media reports suggest that Denis Allex is a pseudonym for the military serviceman.
Hostage Denis Allex died at the hands of his captors, the defense ministry said in a statement.
Allex was an agent of the DGSE, France's equivalent of the CIA and a part of its defense ministry.
Mr Allex appeared in a video in June 2010, appealing to France to drop its support for the Somali government.
BBC: French soldier killed and hostage feared dead in Somalia
The French government has said it believes Mr Allex was killed during the raid, in which two French commandos also died.
Mr Allex, who was kidnapped in Somalia in July 2009, was killed in retaliation for a failed French operation to free him.
The French government has said it believes Mr Allex was killed during last week's raid, in which two French commandos also died.
BBC: Denis Allex: French agent 'killed' by Somalia al-Shabab
But no proof of death has been made public for Mr Allex.
BBC: Somalia's al-Shabab 'to kill' French hostage Denis Allex
The French government, however, says it believes Mr Allex was killed by his captors during Friday's raid in which two French commandos died.
BBC: Somalia's al-Shabab 'to kill' French hostage Denis Allex
Allex was abducted on July 14, 2009, while on a mission in Mogadishu in support of the transitional Somali government, the French Defense Ministry said.
CNN: U.S. supported France's failed hostage rescue in Somalia
On Friday, about 50 helicopter-borne French commandos launched an assault on the al-Shabab stronghold of Bulo Marer, where it is believed Mr Allex was being held.
BBC: Somalia's al-Shabab 'to kill' French hostage Denis Allex
The French Chief of Defence Staff, Adm Edouard Guillaud, told French radio that he believed Mr Allex was already dead and accused al-Shabab of "media manipulation".
BBC: Somalia's al-Shabab 'to kill' French hostage Denis Allex
Allex was abducted on July 14, 2009, while on an official mission in Mogadishu in support of the transitional Somali government, the French defense ministry said.
On Friday, about 50 French commandos launched an assault by helicopter on the al-Shabab stronghold of Bulo Marer, believing Mr Allex was being held in the town.
BBC: Denis Allex: French agent 'killed' by Somalia al-Shabab
Then, French commandos went into action in Somalia, swooping on the town of Bulo Marer in an attempt to free Denis Allex, who was kidnapped in July 2009.
BBC: UK troops to assist Mali operation to halt rebel advance
Al-Shabab said it had advance warning of the attack and Mr Allex - a codename for the French intelligence agent - was not in Bulo Marer at the time.
BBC: Denis Allex: French agent 'killed' by Somalia al-Shabab
The moves came after French forces engaged in a fierce gunbattle with militants in their attempt to rescue hostage Denis Allex, who was a member of the DGSE, France's equivalent of the CIA and a part of its defense ministry.
CNN: U.S. supported France's failed hostage rescue in Somalia
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