Police investigating the unsolved murder of a British family in France 14 years ago have an unexpected new clue with the discovery of a Luger pistol in the waters of a nearby lake.

One of the few certainties in the killings of Saad al-Hilli with his wife and mother-in-law – as well as a passing cyclist – is that they were shot through the head with a Luger model P06, a type used by the Swiss army until around 1960.

Now France’s cold case unit has confirmed the discovery of a Luger in Lake Annecy, in the Alps, not far from the scene of the murders in September 2012.

According to Marianne magazine, which broke the story, it was British tourists on 20 August who found the weapon lying in two metres of water.

At first they thought it was a water pistol, but realised their mistake when they felt its weight.

The discovery was made near the very camping site – Le Solitaire du Lac – where the al-Hillis were staying in their caravan, Marianne reported.

Forensic experts are now examining the weapon, which has been badly damaged by its time under water, to see if it is indeed a P06 model.

It is estimated that around 60,000 Luger P06s were manufactured. But the number of Luger pistols in general that were made is more like three million.

Exhaustive investigations in France and the UK have left police no closer to understanding who carried out the al-Hilli murders and why. Over the years a series of leads have been pursued then dropped.

A British national of Iraqi birth, Saad al-Hilli was holidaying with his family in the picturesque countryside of Lake Annecy in eastern France.

On the afternoon of 5 September, his body with those of his wife and mother-in-law were found in their car, its motor still running, on a forest road near the village of Chevaline. A passing cyclist had – like the other victims – been shot through the head.

Poignantly, the two al-Hilli daughters, aged four and seven, survived. The older girl had been hit on the head with a pistol butt and was badly hurt. The younger, lying in the car under her mother’s skirts, was not discovered till forensic experts began examining the scene many hours later.

It was fragments from the pistol butt which enabled police to identify it as a Luger P06. The model is regarded more as a collector’s item than a working weapon, which made the theory of a professional hit against the family seem less likely.

Lake Annecy is only 50km from Switzerland, where the Luger P06 will have been familiar to older people from their military service. French police said many examples of the gun have been kept by families on either side of the border.

Among the theories that have been entertained are that the murders were linked to a family row over money; that they were the work of a motiveless crank; and that the main target was the cyclist.

Police were also briefly intrigued by the fact that al-Hilli’s wife’s first husband – an American – died of a heart attack just hours before the killings in France.