Sixteen people were wounded, two seriously, along with the three killed in Friday's shooting spree in southwest France by a man claiming allegiance to the Islamic State group, President Emmanuel Macron said.
The injured included the driver of the hijacked auto as well as a police officer who was out jogging with colleagues in Carcassonne.
A gunman who took several hostages in a supermarket in the southern French town of Trebes has been identified as a Moroccan-born petty criminal who was not previously thought to be a terrorist threat.
A gendarme who was shot three times after voluntarily taking the place of a hostage during a supermarket siege in southwestern France on Friday has died, France announced on Saturday.
If the link to Islamic State is confirmed, the hostage-taking would be the first deadly attack in France since October, when two young women were stabbed to death outside Marseille's main train station.
The shooter killed a driver in Carcassonne (located in southern France) and stole his auto.
About 50 people were in the store at the time, and Lakdim quickly opened fire, killing a customer and an employee, Molins said. When shots rang out, elite police stormed the building to kill the assailant. "He then withdrew back into the supermarket".
Despite this, Paris prosecutor Francois Molins there was "no warning sign" that Lakdim would carry out an extremist attack.
Two others were wounded at the market, an Interior Ministry spokesman said.
"All the information we now have leads us to believe it is a terrorist act", Prime Minister Edouard Philippe said while on a visit to Mulhouse in eastern France, cutting short the trip.Interior Minister Gerard Collomb was on his way to the scene.
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He was in a stable condition, Prime Minister Edouard Philippe said.
But there was a high risk from home-grown attackers, he said: "That is, you have a lot of individuals who have self-radicalized, with various psychiatric profiles; some of them are pathological, others not", he said.
He acted alone, Collomb said.
As he drove away, Lakdim came across four riot police officers who were out jogging.
"They managed to get some of the people out", he said, but the attacker kept one hostage back as a human shield.
Carole, who was shopping at the supermarket, said people hid in a cold room.
A total of three people were killed and three people were injured by the gunman.
Arabic for "God is great" - and proclaimed himself a "soldier of the Islamic State" as he stormed into the small-town supermarket.
Speaking later outside the store, the French Interior Minister, Gerard Collomb, described how police intervened immediately after the siege started at around 11am.
Heavily armed police also searched Lakdim's apartment in Carcassonne to search for clues as to his motives and weapon source.
Mr Macron said of the police officer: "In offering himself as a hostage to the terrorist holed up in the Trebes supermarket, Lieutenant Colonel Beltrame saved the life of a civilian hostage, showing exceptional self-sacrifice and courage".