She was reportedly killed while playing in the garden of her home in Saint-Herbot, a village in Brittany, at about 10pm local time on Saturday.

According to France 3, her father is in a critical condition, while her mother has non-life-threatening injuries.

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

Local residents said she ran to other neighbours and shouted "my sister is dead, my sister is dead".

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."

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

The Times reports that the family was having a barbecue at the time - and their 71-year-old neighbour, who is Dutch, has been arrested on suspicion of killing her. His wife is also being held.

According to local prosecutors, initial evidence suggests the pensioner "suddenly emerged armed with a gun and fired several times towards the victims".

It has also been suggested that the neighbours may have had an ongoing dispute.

A negotiator persuaded the pensioner and his wife to give themselves up before they were detained.

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."