The French presidency in Paris said it had received "no confirmation" of the killing of Germaneau, and was trying to verify the claim.
Sarkozy called a crisis meeting of his defence and security advisers for Monday.
Mauritanian troops, backed by French special forces, launched the cross-border raid against an AQIM base in Mali on Thursday and continued the assault for several days.
The raid into Mali was a sign of an escalating European and African response to the armed group.
Mauritanian officials have said six fighters were initially killed and a seventh later died of wounds.
The military operation appeared to anger Mali, which was not involved, and Spain, which also has hostages held by another al-Qaeda faction in the region.
Paris has indicated that both those countries were informed in advance.
Germaneau was kidnapped in northern Niger on April 19 and the next month his abductors issued a photograph of him as well as a taped message in which he appealled to Sarkozy to work for his release.
He said he suffered from a serious heart illness and had no more medication and that he was struggling with the heat.
Germaneau's Algerian driver, who was also abducted, was later released. He said the Frenchman was being held in a desert zone in Mali.
On July 11, AQIM gave France a 15-day deadline to help secure the release of its members in the region, warning that Germaneau would be killed if Paris failed to comply.
Current and former security officials in Algeria, which has the most experience with AQIM because it grew from a group that originated there, had warned that the raid could put the French hostage in danger and criticised French involvement.
One Algerian security official said the operation would help the fighters recruit more followers by allowing them to cast their campaign as a battle against Western "infidels" and not just fellow Muslims.
"The failure will be used by the extremists to spread their anti-Western propaganda," the security official, who did not want to be identified because he was not authorised to speak to the media, told the Reuters news agency.
A former Algerian security official said: "France failed to release its hostage. It failed to eliminate Abu Zeid....
"It angered the terrorist group, which will now either demand a ransom or kill the hostage if it has not done it already."
AQIM killed British captive Edwin Dyer last year after Britain refused to give in to its demands.
Last April, French troops attacked pirates who seized a yacht off the coast of Somalia. One hostage died and four were freed.