Hundreds of security forces were hunting a gunman who opened fire near a Christmas market in the eastern French city of Strasbourg.
Two people were confirmed dead, while a third was brain dead following the December 11 incident, Prosecutor Remy Heitz said.
Heitz said the suspect also left 12 people injured, using a handgun and a knife to attack his victims.
The man cried out "God is great!" in Arabic during the attack, the prosecutor said, adding that he was shot in the arm during an exchange of fire with soldiers.
The suspect, a 29-year-old from Strasbourg, was on a watch list of suspected extremists.
Interior Minister Christophe Castaner said border controls were strengthened and security at all Christmas markets will be stepped up.
The country has raised its security-alert level, he also said.
Security has been stepped up in recent years after a series of attacks in France by Islamist militants since 2015.