Authorities believe the killing of a teacher in France is probably linked to the ongoing war between Hamas members in Gaza and Israel.

A Chechen-origin attacker, who has been arrested, stabbed to death a teacher at Gambetta High School in the northern city of Arras in France on Friday.

According to reports, two others were injured in the incident.

Witnesses say the attacker shouted "Allahu Akbar", or "God is greatest", during the attack, reported BBC.

French President Emmanuel Macron visited the school and condemned the "barbarity of Islamist terrorism", reported the British media.

He said police had averted another attempted attack in another part of France.

The attacker, named as 20-year-old Russian national Mohamed Mogouchkov, is of Chechen origin and known to the security services for his involvement with Islamist extremism, according to police as reported by BBC.

Interior Minister Gerald Darmanin later said there was "probably a link between what's happening in the Middle East and this incident" in Arras, AFP news agency reported.

France has upped its alert level to the highest position following a crunch security meeting chaired by Macron later Friday, the prime minister's office told AFP.

According to reports, eight people have been taken into custody in connection with the incident.

In addition to the attacker, several members of his family were arrested "for the purposes of the investigation", including one of his brothers and his sister, police sources told AFP.