0253 GMT September 23, 2018
The attack took place just before 23:00 (21:00 GMT) on the banks of a canal in Paris's 19th district, BBC reported.
People playing a game of pétanque nearby threw balls at the attacker to try to stop him.
The man, said to be Afghan, was later arrested. The incident is currently not being treated as a terrorist attack.
The man initially stabbed two men and a woman near the MK2 cinema on the quai de Loire, along the Ourcq canal, reports say.
Eyewitness Youssef Najah, 28, said he was walking beside the canal when he saw a man running and holding a knife about 25-30cm (10-11 inches) long.
"There were around 20 people chasing him. They started throwing pétanque balls at him," he said.
"Around four or five balls hit him in the head, but they weren't able to stop him," he added.
The man then reportedly attacked the two British tourists in a nearby street.
Image caption Police cordoned off the area after the attacks
"We are urgently investigating this incident and are in close contact with the French authorities," the UK Foreign Office said in a statement.
A French police source said: "At this stage, there is nothing to indicate that it could be a terrorist attack."
There have been several knife attacks in France over the past few months, but few have resulted in terrorist investigations.