PARIS (Reuters) - A British father killed in the French Alps last month made a desperate bid to drive his family to safety under a hail of bullets, but his car got stuck on a verge and the gunmen moved in to finish them off at close range, police believe, according to newspaper Le Monde.

Saad al-Hilli, an Iraqi-born British engineer, was found shot dead with his wife and mother-in-law in their BMW car on a remote mountain road near the village of Chevaline, not far from the Swiss and Italian borders.

A French cyclist was also found shot dead though police have not established whether he was killed first or became a victim after coming across the scene on his bike.

Although the investigation has shed some light on the sequence of events, many key details as well as the killer's motive are still eluding police, the newspaper said on Saturday.

The gunmen also tried to kill the British family's seven-year-old daughter, beating her around the head after he had run out of ammunition.

Her four-year-old sister survived by hiding beneath the legs and skirt of her dead mother in the backseat of the car.

Investigators believe the killer was alone and used only one weapon, a pistol common in the Swiss army in the 1920s and 1930s, and not the sort of weapon used by professionals, Le Monde said.

The older girl told police she and her father were outside the car when the shooting started. Unable to get her into the car, he then attempted to escape in the vehicle with the rest of the family under fire from the killer.

However, as he backed up to get away, the vehicle became stuck when its tyres lost their grip on an embankment, leaving the family at the mercy of the killer who then shot the three adults in the head.

The newspaper said that while it is unclear at what point the cyclist was killed, it appears his body was hit by al-Hilli's car during the attempted escape.

After running out of ammunition, the killer hit the older girl in the face with the gun, but was apparently interrupted by someone or something before fleeing the scene.

The prosecutor working on the case, who was not immediately available for comment on the report, has said the solving the case could take years.

(Reporting by Leigh Thomas and Thierry Leveque; Editing by Jon Hemming)