An official narrative of the Alps murders, published yesterday, suggests that the quadruple killer was probably a lone psychopath, rather than a professional assassin.

A blow-by-blow gendarmerie account of the 15 brutal minutes above Lake Annecy on 5 September – including many facts previously undisclosed – was leaked yesterday to the French newspaper Le Monde. The narrative, based on seven weeks of investigations, says that the gunman first opened fire on a group of three people standing in a forest lay-by: a local cyclist, Sylvain Mollier, 45; a British tourist, Saad al-Hilli, 50; and his daughter, Zainab, aged seven. The murderer also fired at Mr al-Hilli's wife, Iqbal, 47, and her mother, as they sat in the back of the family car.

Mr al-Hilli, already wounded, fled to his car, pulling his daughter by the hand. As he tried to turn the BMW around, he ran over and dragged the body of the wounded cyclist under his wheels. Still under fire from the gunman, Mr al-Hilli rammed the back of the car into the steep forest side and became jammed there.

The gunman, using an obsolete, pre-war Luger P06 automatic pistol, then approached the car and shot Mr and Mrs Al-Hilli and Suhaila al-Allaf, 74, twice each in the head. It is also believed that he may have returned to the cyclist's body to finish him off.

Seven-year-old Zainab al-Hilli, who has helped investigators more than previously revealed, owes her life to the fact that the killer ran out of bullets, the report says. The attacker beat her savagely over the head with the butt of his gun and left her for dead. Fragments of the gun, as well as 22 cartridge cases, were found at the murder scene.

Zainab, now recovering with relatives in Britain, has told investigators that she and her father were outside the car when the gunman opened fire. She said her father dragged her towards the car, but she was unable to get inside. The 7.65mm gun used by the killer was issued to the Swiss army in the 1920s and 1930s. It is mostly regarded as a collector's piece and is not the kind of weapon used by professional killers, the report said.

The sequence of events established by the report suggests that the French cyclist, Mr Mollier, was the first victim to be seriously injured but was not necessarily the first target. Study of spent cartridges and bullet wounds by forensic experts suggests that the gunman fired a first volley of shots toward the cyclist, Mr al-Hilli and his daughter, and the parked car.

Investigations of a possible motive for a targeted killing of Mr al-Hilli – including a family quarrel over money and his work on micro-satellites – have revealed nothing special, Le Monde said. The Annecy area prosecutor, Eric Maillaud, told Le Monde: "The hypothesis of a lone and psychologically disturbed killer, is gaining ground."