An 11-year-old girl has been shot dead while outside her home in Brittany, western France, following a years-long dispute between neighbours over land, the local prosecutor said.

French media reported the girl was British. A spokesperson for the British embassy in Paris did not immediately respond to telephone calls.

The family were enjoying a warm evening on Saturday in their garden in the small village of Saint Herbot, near Quimper, when a Dutch neighbour shot at them several times, the prosecutor said.

The girl's parents were both hurt, with her father suffering life-threatening wounds, the prosecutor said. The couple's second daughter, aged 8, was unharmed but in a state of shock.

"Initial evidence suggests the victims' neighbour, a 71-year-old Dutch pensioner, suddenly appeared armed with a firearm and fired several shots in the direction of the victims ... before retreating to his home with his wife," the Quimper prosecutor's office said in a statement.

The Dutchman surrendered when a police negotiator coaxed him out of his property.

The local prosecutor said the motive was not immediately clear but that the two families had been embroiled in a years-long row over a plot of land adjoining the two properties.

The family had lived in the village for several years and always attended the local village fete, local media reported.

The case has been handed to the public prosecutor in Brest given its gravity.

The shooting comes just days after a British toddler was among four children and two adults stabbed in the tranquil town of Annecy in the Alps.