A fifth victim – a young girl – is fighting for her life in hospital.
The bodies of two women and a man were first found in a BMW four-wheel-drive vehicle in a parking area close to a forest park near Chevaline.
The fourth body – a male cyclist – was found near to the scene at Lake Annecy, known as the "little Venice of the Alps". The area is a popular tourist destination known for its swimming and water sports.
French police say the young girl suffered serious gunshot wounds to her head and was rushed by helicopter to Grenoble for emergency treatment. Police believe the girl – thought to be aged under 10 – and the three victims found in the car were possibly members of the same family.
A Foreign Office spokesman said: "We are aware of the reports of the shooting and we are looking into this urgently."
The macabre discovery was made by a cyclist at around 3.30pm local time in a remote car park.
The parking area in which the bodies were found is in a quiet, forested area in the small community of Horses, which overlooks Lake Annecy. It has been sealed off by 60 police who are scouring the area for clues. Forensic officers are also examining a number of bullet holes that pierced the car.
No weapon was found in the vehicle and police could not speculate on the reasons for the shooting. They did, however, confirm that of the bodies found in the BMW, the man was found in the front and the two women were lying on rear seats.
The identity of the cyclist has not been revealed but police believe he may have tried to intervene during an armed robbery attempt on the family.
An Albertville police spokesman said: "This car was parked in an area that is the starting point for hiking, a little away from people's homes.
"We are looking at the possibility that the three dead people in the car and the young girl were all from the same family.
"The entire area has been sealed off, while a full multiple murder investigation is under way."
Three months ago, Chevaline was the scene of a gruesome discovery when human bones were found at the edge of a wood.