Police have arrested a man in connection with the incident, which happened on the banks of a popular canal in the northeastern district of Quai de la Loire at just after 11pm local time on Sunday.
The suspect was said to have been wielding a blade and an iron bar when he targeted people, with four of the victims suffering severe wounds and all seven taken to hospital for treatment.
French broadcaster BFMTV and newspaper Le Parisien reported that one of the Britons was stabbed in the head.
The Foreign Office said it was aware of the reports, but offered no further information.
Citing a judicial source, news agency Reuters said there was no initial sign the attack was linked to terrorism.
Quai de la Loire runs alongside the popular Villette Canal Basin and boasts a number of restaurants and cinemas.
The Paris Tourist Board lists it as also having several cafes and libraries, and says it is particularly lively during the summer months.
News Source SkyNews