French commandos, acting with Mauritanian troops, had tried to free Michel Germaneau, a retired engineer kidnapped on April 20 in Niger, but had not found him when they raided a desert Al Qaeda camp in Mali, Sarkozy said.
"I condemn this barbarous act, this odious act, which has just left an innocent victim," the president said in a live televised statement. "Far from weaking our determination, his death must reinforce it."
He urged French citizens to avoid travel to the Sahel region and vowed: "This crime will not go unpunished."
A leader of Al-Qaeda in the Islamic Maghreb (AQIM) said in an audio recording aired by Al Jazeera on Sunday that the group had killed Germaneau on Saturday in revenge for the killing of six group members in the raid.
Sarkozy said France had received no sign since May that Germaneau was alive, and had intervened after AQIM threatened on July 11 to kill him within two weeks unless Paris arranged a prisoner exchange.
Germaneau,who was working as a volunteer building a school for Tuareg nomads, was believed to be in the hands of Abdelhamid Abou Zeid, leader of the more hard-line of two AQIM factions operating in the Sahara.
The same AQIM wing killed British captive Edwin Dyer last year after Britain refused to give in to its demands.
Sarkozy said he had asked Foreign Minister Bernard Kouchner to visit Mali, Niger and Mauritaria from Monday evening to discuss increased security measures for French nationals in the region.
