The girl’s father was also shot – during what is believed to be a neighbourly dispute – and is in a critical condition, according to the La Telegramme news website.
The family had been living in the small village of Saint-Herbot in the region of Brittany, for the past few years, local prosecutor, Carine Halley, told French media.
There had been a conflict for some time with their neighbours over a plot of land adjoining their properties, Halley said.
On Saturday evening, the 11-year-old girl and her eight-year-old sister were playing in their garden when a man appeared and allegedly fired shots into the yard.
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The younger sister was not harmed, but the girls’ father was also hit with one of the bullets.
Police have arrested a 71-year-old Dutch man.
The UK’s Foreign Office said it was providing assistance to a British family after a shooting in France, the BBC reports.
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