TRÈBES: A gunman claiming allegiance to the Islamic State (IS) group killed three people in a shooting spree and supermarket hostage siege in southwest France on Friday before anti-terror police shot him dead.

Five people were also shot and wounded in France's first major militant attack since October, including a heroic policeman who offered to take the place of hostages being held at the supermarket.

"Our country has suffered terrorist attack," President Emmanuel Macron said in a televised address following the rampage in the medieval town of Carcassonne and nearby Trebes.

The Islamic State group claimed the attack was in response to its call to target Western enemies -- as is customary when the assailant has pledged allegiance to the militants.

The shootings come as France remains on high alert following a string of deadly attacks that have killed more than 240 people since 2015.

Top anti-terror prosecutor Francois Molins named the gunman as Radouane Lakdim, a 25-year-old who had convictions for carrying a banned weapon and for drug use.

"He had been on a watchlist for his radicalisation and links to the Salafist movement," Molins told reporters in Carcassonne, adding that Lakdim had been tracked for his online contacts with extremists.

Security sources said Lakdim was born in Taza in northern Morocco and held French nationality. His partner, who lived with him in Carcassonne, has been detained, Molins said.

Lakdim started his rampage in Carcassonne at around 10.30 am (0930 GMT), hijacking a car and shooting the two people inside, Molins said. The passenger was killed, and the driver remains in a critical condition.

Lakdim then shot and wounded a police officer who was out jogging with colleagues before driving to the Super U supermarket in nearby Trebes.

"The attacker entered the store shouting "Allahu Akbar" (God is greatest) and saying he was a soldier of the Islamic State, ready to die for Syria," Molins said.

He further demanded "the release of his brothers" from prison before shooting a supermarket customer and an employee dead.

"I was five metres away from him," the store's security guard said, speaking on condition of anonimity.

"He shot at me twice." Luckily for the security guard, "he shot badly."