The incident occurred in the town of Le Port-Marly, approximately 20km west of Paris.
A 73-year old man and a 57-year old woman are believed to be in a critical condition after being shot in a supermarket on Monday afternoon.
According to local media reports, a man in his 70s opened fire in a supermarket in the town of Le Port-Marly, before fleeing and seeking refuge in a nearby house, which has since been surrounded by police.
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A spokesman for the prosecutor’s office said that the incident was a private dispute and “in principle not a terrorism issue”.
The suspect is believed to be known to police and has a history of violent behaviour.