The French Foreign Minister, Laurent Fabius, said Yann Desjeux died when the Algerian military launched a rescue operation at the remote gas plant at In Amenas.
Three other French citizens were rescued.
It is understood Desjeux comes from the town of Anglet, in the Pyrénées-Atlantiques department in southwestern France where he also runs a restaurant.
The crisis began on Wednesday when militants attacked the site, which is jointly run by the British energy giant BP, Norway’s Statoil and Algeria’s state-owned energy company Sonatrach.
A security source in Algeria earlier said 12 hostages have been killed since the Algerian army launched the operation against the Al Qaeda-linked hostage takers.
The office of the French President says François Hollande will on Sunday meet the families of French hostages held in the Sahara.