An 11-year-old girl from a British family who was shot dead in the garden of her home in France has been named as Solenne Thornton.

The child was killed while playing outside her home in Saint-Herbot, a village near the city of Quimper in Brittany, at about 10pm local time on Saturday.

The family were enjoying the warm evening when a Dutch neighbour allegedly shot at them several times, the local prosecutor said.

Town hall officials said there had been issues between the neighbours over "a hedge" and the village was "in 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.

According to local television network France 3, the girl's father, Adrian Thornton, is in a critical condition, while her mother has non-life-threatening injuries. Both parents are reportedly in their 40s.

The victim's mother and sister were named as Rachel and Celeste Thornton.

The girl's sister - who is eight years old - managed to escape unhurt and raised the alarm, but is in a state of shock.

It is believed the family had lived at the property for four or five years - and both girls were born in France.

The suspect has been arrested on suspicion of killing the girl, according to local prosecutors. His wife is also reportedly being held.

Local media has reported the family was having a barbecue at the time of the attack.

Yannick, a local resident, told the daily regional paper Le Telegramme de Brest: "We heard the bangs and we thought it was children playing with bangers. Then the kid ran into a neighbour's house saying: 'My sister is dead, my sister is dead'."

The Intervention Group of the National Gendarmerie tactical unit was called to the scene and a negotiator persuaded the neighbour and his wife to give themselves up before they were arrested, said Carine Halley, the state prosecutor in Quimper.

She added the attacker's motive is not yet known but it would appear the two sets of neighbours had been engaged in a long-running dispute over a plot of land adjoining their properties for several years.

One neighbour said the dispute with the pensioner began when they "cut down all the trees that bothered them".

A neighbour told La Telegramme he had earlier seen the whole family under the oak tree at the bottom of their garden.

"The two little girls were playing... the parents were sitting on their usual bench and having a barbecue," he said.

Plonévez-du-Faou's mayor, Marguerite Bleuzen, said: "We knew the family well. There is a village fête every year and they always came.

"They are not a family who caused problems. Perhaps there was a dispute with the neighbour, I don't know about that.

"But it is incomprehensible to have shot a child. No one can understand how that could have happened."

Regine Guillot, secretary of the town hall in Plonevez-du-Faou, said the family had lived in the hamlet for five years and added: "There were neighbourhood issues, yes, a hedge, a field, but nothing more than that, not that we were aware of.

"The village is in shock."

A spokesperson for the Foreign, Commonwealth and Development Office said: "We are providing consular assistance to a British family following a shooting in France and are in contact with the local authorities."