"The person had been fighting for their life," an official in the prosecutor's office said on Friday.

Gunman Cherif Chekatt, 29, was killed in the Neudorf neighbourhood of Strasbourg on Thursday night after firing on police, ending a two-day manhunt that involved more than 700 members of the security forces.

The city's traditional Christmas market was reopened under heavy security on Friday.

Stall-holder Bernard Kuntz said the market was reopening just in time for struggling business owners.

"We were getting worried. Some of the guys have taken out loans to be here, and we've already lost two days," he said.

Strasbourg Mayor Roland Ries said the attack was indisputably an act of terrorism.

Strasbourg's cherished Christmas market is a target full of religious symbolism, and the killings have evoked France's difficulties in integrating western Europe's largest Muslim minority and dealing with homegrown militants inspired by Islamic State.

Ries expressed relief that Chekatt had been killed and said everyone in Strasbourg, on eastern France's Rhine river border with Germany, felt the same.

French troops, who have been used to bolster national security since a wave of Islamic State-inspired attacks began in France in 2015, stood guard at the open-air market.

"I think it will help to get back to a life that I would describe as normal," Ries told reporters after the news that Chekatt had been killed.

"With the death of this terrorist ... citizens, like me, are relieved."

Islamic State claimed Chekatt as one of its soldiers, saying he carried out the operation in response to calls for citizens of coalition countries that are fighting the militant group.

IS provided no evidence for the claim and French Interior Minister Christophe Castaner called it "opportunistic".

"Nothing indicates that (Chekatt) was part of a network. There is nothing to suggest that he was being protected by such, but the investigation is not yet over," Castaner told Europe 1.

He described Chekatt as a long-time delinquent whose Islamic beliefs were radicalised during previous periods in prison.

Police were still interrogating seven associates on Friday, including Chekatt's parents, to determine whether he had accomplices.

France ramped up its security threat to its highest level after Chekatt struck late on Tuesday.

Prime Minister Edouard Philippe promised an extra 1800 troops would be put on patrols with a special focus on Christmas markets.

The outdoor market in Strasbourg, centred around a towering Christmas Tree in Place Kleber, draws more than 2 million visitors each year.

Christmas markets have been a feature of the Alsatian city since the early 15th century.

The Strasbourg shooting was the latest in a succession of attacks linked to Islamist militancy in France going back to 2012.

Since January 2015, more than 240 people have been killed in attacks on French soil, most of them in 2015-16.

Australian Associated Press