A fourth body, apparently a person who had been riding a bicycle, was found nearby.
A badly injured 8-year-old girl, also found nearby, was taken to hospital by helicopter, he said.
The car was in a parking area off a road that winds through hills near Annecy lake, not far from the French border with Switzerland.
Maillaud said forensic experts would work through the night at the site and that the three dead in the car included a man, who was in the driver's seat, and two women in the back seat. The fourth victim was wearing cycling gear.
"For now we've not got a lot of elements to go on, bar the fact that it's a dramatic event," he told reporters.
A British foreign ministry spokesman said: "We are aware of the reports of the shooting and we are looking into these urgently."
