A police source, who asked not to be named, told AFP that the authorities were not at this point looking at terrorism as an explanation and the case has not been referred to national anti-terror prosecutors.
The body of the woman was found in the Mediterranean resort of Agde in the Hérault département of southern France, the police source said.
Police had visited her home after the woman’s son raised concern he had not heard from her despite usually making daily calls. He was also connected to her home via video link and said he had seen a shadow on the ground.
According to another source, the victim’s head was on a table next to the body. There was no sign of a break-in, the outside gate was closed and the front door of the house unlocked.
There were no immediate further details and police did not at present favour one particular theory over what happened, police said.