The Dutch tourist, who was the car's passenger, was hospitalised after he was shot in shoulder as his car travelled along the A63 in Landes, south west France.
Prosecutors in Mont-de-Marsan told France Bleu that the local hunt was in the area at the time hunting wild boar and they believe this was a hunting accident, although no suspect has so far been identified.
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The 61-year-old tourist's wounds are not life-threatening.
If confirmed, the accident would be the third so far this season in the Landes area since the start of the hunting season in mid September.
Every year dozens of people are injured by la chasse in France and deaths from stray bullets are not unusual.
Once the hunting season opens, anyone in rural areas of France is advised to keep a very careful look out for local hunters and for signs that indicate hunting is taking place in the area.