A person known to the French authorities as a radical Islamist with mental health problems stabbed a German tourist to death and wounded two people in central Paris on Saturday before being arrested, officials said.

The attack took place close to the Eiffel Tower during a busy late weekend night and came with the country on its highest alert for attacks as tensions rise against the background of the war between Israel and Hamas.

"We will not give in to terrorism," Prime Minister Elisabeth Borne wrote on X, formerly Twitter, after the attack.

French anti-terror prosecutors said that they would now take on the investigation.

The attacker was known to authorities as a radical Islamist and was being treated for mental illness, a police source told AFP.

He shouted "Allahu Akbar" ("God is greatest") before being arrested, the source added.

The Paris prosecutor's office said the attacker is French, born in 1997, and has been arrested in an investigation into murder and attempted murder.

Interior Minister Gerald Darmanin who visited the the scene by the River Seine's Bir Hakeim bridge said the man had already been sentenced in 2016 to "four years in prison" for planning another attack which he failed to carry out.

"A man attacked a couple who were foreign tourists. A German tourist who was born in the Philippines died from the stabbing," he said.

A taxi driver who witnessed the scene intervened, Darmanin said. The attacker then crossed the Seine attacking others and injuring one with a hammer, while police chased in pursuit.

Police used a taser to neutralise the man who was then arrested.

"He had threatened them very violently... he will now have to answer for his actions before justice," Darmanin said.

The suspect told police he could not stand Muslims being killed in "Afghanistan and Palestine", according to the minister. (AFP)