Local press reported that a gunman on a scooter opened fire at around 9:00 pm (1900 GMT) in the La Reynerie district of Toulouse.
"No possibilities are ruled out, but there is at this stage no indication of any terrorist element" connected to the incident, the official added.
The favoured theory is that the shooting was a revenge killing, a source close to the enquiry said.
Local officials, meanwhile, said extra security had been deployed to the area.
Last year La Reynerie district, in the southwest of Toulouse, was the scene of two shooting incidents, both believed to be a settling of scores.
In one incident last July a Russian man of Chechen origin was shot dead by an unknown gunman on a scooter.