The leader of the Al-Qaeda affiliate Abu Musab Abdul Wadud says the organisation killed Michel Germaneau to avenge the killing of six Al-Qaeda fighters in a failed French rescue operation.
"Sarkozy failed to free his compatriot in this operation but he has, without any doubt, opened for his people and for his country one of the gates of hell," Wadud warned.
The retired engineer was working with an aid agency to improve health services and schools at the time of his kidnap in Niger in April.
French officials say they had received no confirmation of his death and were trying to verify the claims.
In May, his abductors issued a photo of an exhausted-looking Germaneau, together with a taped message in which he appealed to Sarkozy to work for his release.
On 11 July, the al-Qaeda militants gave France a 15-day deadline to help secure the release of its members in the region, warning that the hostage would be killed if Paris failed to comply.
On Thursday, Mauritanian troops backed by the French army launched a cross-border raid on a remote al-Qaeda camp in the Malian desert to rescue the hostage.
Documents, bomb-making equipment, guns and ammunition were found during the
raid but soldiers found no evidence that Germaneau had been held there.
Prime Minister Francois Fillon, Interior Minister Brice Hortefeux, Foreign Minister Bernard Kouchner and Defence Minister Herve Morin, have been convened to a meeting on Germaneau.