Police surrounded a building, believed to be the suspect's home, after he fled the scene of the attack outside the Super U store in Port-Marly, about 20km west of Paris.
A police official said the man quickly handed himself in following the incident, which took place at around midday.
Reports on the suspect's age have varied, but he is be understood to be a man in his 60s or 70s who is already known to officers.
France is on high alert following recent extremist attacks. However, a spokeswoman for the Versailles public prosecutor's office said the incident did not appear to be an act of terrorism.
"He went home and the RAID (elite police) is readying for negotiations with him," she added.
The victims are said to be a 57-year-old woman and a 73-year-old man, wounded in what prosecutors have described as "a private dispute".
According to French news channel BFM TV, they are both seriously injured and are being treated in hospital.
The Local reports that a rifle was found in the suspect's car.