Four of the victims were in a critical condition, police said, after the man brandishing a large blade and and iron bar went on the rampage next to a canal in the northeast of the capital.
The suspect is believed to be an Afghan national and has been arrested, said a source close to the enquiry, adding he had targeted “strangers” but that “nothing at this stage shows signs of a terrorist nature”.
Chaos erupted on the banks of the Bassin de la Villette, an area popular with locals and visitors who frequent the cafes, cinemas and other cultural venues along its banks, just after 11:00pm (2100 GMT).
Eyewitness Youssef Najah, 28, said he was walking beside the canal when he saw a man running and holding a knife about 25-30 cm (10-11 inches) long.
“There were around 20 people chasing him. They started throwing petanque balls at him,” Najah said, referring to the sport popular in France also known as boules.
“Around four or five balls hit him in the head, but they weren't able to stop him,” he added.
According to the same witness, the attacker then dived into an alleyway, where the man “tried to hide behind two British tourists. We said to them: 'Watch out, he has a knife”. But they didn't react”.
The pair were then attacked, he said.
A security guard at one of two cinemas on either side of the water said he had seen the attacker running away from two men who were trying to stop him.
“He had an iron bar in his hand which he threw at the men chasing him, then he took out a knife,” he told AFP.
The UK foreign office said it was aware of reports of the attack and was “urgently investigating this incident” in cooperation with French authorities, British media reported.
A police investigation has been launched for attempted murder, according to a judicial source.
It is the latest of several knife attacks France has seen in recent months, with terrorism being ruled out in most cases.
On August 23, a man stabbed his mother and sister to death and seriously injured another person in a town near Paris before being shot dead by police.
The motive for the violence remained unclear despite a claim by the Islamic State (IS) group that it was an attack by one of its fighters responding to the terror organisation's propaganda.
Authorities said the 36-year-old had serious mental health problems and had been on a terror watch list since 2016.
That attack came days after an Afghan asylum-seeker was arrested in town of Perigueux for a drunken rampage with a knife in which four people were wounded, one seriously.
Police said investigators had “very quickly” dismissed a terrorist motive after the August 13 incident.
And on June 17, two people were hurt in another southern town when a woman shouting “Allahu akbar” (God is greatest) attacked them in a supermarket with
a boxcutter knife.
France has been on high alert following a string of jihadist attacks in recent years, often by people who have become radicalised or claim to have acted in the name of the IS group.
More than 240 people have been killed by Islamist extremists since a massacre at the Charlie Hebdo satirical magazine in Paris in January 2015.