The attack reportedly unfolded around 10.45pm local time.
A witness playing petanque is said to have made an attempt to foil the attack by throwing a boule at the assailant.
Four of the people are said to be seriously injured, while the suspect is an Afghan national.
The victims were all rushed to local hospitals, where their conditions were described as "serious but not life threatening". The attacker is not thought to have been badly injured by officers.
There was no initial sign that the attack was linked to terrorism, a judicial source said.
"Nothing at this stage shows signs of a terrorist nature in these assaults," the source close to the inquiry said.
The case is being investigated by judicial police, with Paris prosecutors opening an official inquiry.