The girl was hit by several pieces of shrapnel while walking with her mother past a church in Moosch, Haut-Rhin, where a wedding was taking place.
According to a prosecutor, the shots were fired by a 60-year-old wedding guest in celebration and were not aimed at the girl.
"He pulled the trigger three times but the gun didn't work," said the prosecutor, according to French news site L'Alsace.
"So he dropped the gun to the ground and that's when it went off."
(The village of Moosch in eastern France. Photo: AFP)
The girl was hit in the thighs and arms, and taken immediately to hospital. While her injuries are not life threatening, her wounds are likely to have leave her with cosmetic damage, the prosecutor added.
The gunman was held in police custody for 24 hours before he was released. He has also been summoned to the criminal court for unintentially causing injury to another.
Celebratory gunfire claimed the life of another French person this year. In June, a young woman died after being shot in the head while attending a wedding in northern France. She was in the street at the time, and was hit by celebratory shots fired from a procession of cars involved in another wedding.