The incident took place just after 11.00pm local time on the banks of a canal in the north-east of the capital.
The suspect, believed to be an Afghan national, has been arrested, sources told news agencies.
A security guard at one of two cinemas on either side of the Canal de l’Ourcq said he saw a man who had already assaulted people being chased by two other men who tried 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 said.
Police said four of the seven wounded are in a critical condition.
One of the British tourists suffered a chest injury, while the orther was stabbed in the head, Le Parisien newspaper said.
The UK Foreign Office said it was investigating the incident.
Police said they were not treating the incident as a terrorist case at this stage.
Mounir Mahjoubi, the junior minister for digital affairs in the French government, who was elected to parliament last year in the district that includes the 19th arrondissement, expressed thanks on Twitter for “the people who intervened against the attacker.”