He fled when several people threw metallic pentaque balls at him.
Of the seven wounded, four are in a critical condition, police said.
The Britons, believed to be tourists, were said to have been walking in Rue Henri Noguères when they were attacked.
Eyewitness Youssef Najah, 28, told the BBC: "There were around 20 people chasing him".More news: First task for Packers RT Bryan Bulaga: facing Bears’ Mack
The paper said the perpetrator stabbed three people near a cinema on the Bassin de la Villette, and men playing pétanque nearby attempted to stop the man, with one throwing a ball at him.
A man was arrested by police following the incident, and is now being held in custody.
One of the British tourists was stabbed in the head, while the other was "cut in the chest", reports suggested.
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.More news: The Black Ops 4 Blackout Gameplay Trailer Actually Looks Pretty Good
Police officers work on the scene of a knife attack in Paris, Monday, Sept. 10, 2018.
"Nothing at this stage shows signs of a terrorist nature in these assaults", the source said, adding that the attacker had targeted "strangers in the street".
France has seen smaller lone-wolf attacks in recent months.More news: Rodgers returns from injury, leads incredible comeback over Bears