The incident happened in the town of Villejuif, about four miles south of the French capital.
Four people are believed to have been stabbed including two who are reported to have died.
The attacker was chased by police and then shot nearby. Some reports suggest the man was wearing an explosive vest although this has not been confirmed.
The BBC reports that four people are thought to have been stabbed, with two reported to have been seriously injured.
The attack took place outside a supermarket and the targets appear to have been chosen at random.
Police have advised people to avoid the area, which is near to the Hautes-Bruyères state park.