The relics were recovered by police in February after an amateur diver came across the skull while searching for sea urchins just off the rocky Cap d'Antibes promontory.
Nine months later, DNA testing has enabled investigators to establish that one of the bones, part of an arm, belonged to Stephane Hirson, a psychologically disturbed teenager who disappeared from his home near Paris in February 1994.
But they have been left scratching their heads over the origin of the other bones, which they have established came from another man, two women and possibly one other person.
The skull, which came from a man aged at least 50, has proved particularly intriguing as it had a target sign drawn on it, together with the words "death to pedophiles" written in indelible ink.
"We are faced with a series of mysteries," admitted Georges Gutierrez, the prosecutor in the town of Grasse who will lead the investigation.
The opening of a murder probe enables local authorities to allocate more resources to try and get to the bottom of the mystery.
Further forensic tests are to be carried out to try and establish how long the bones had been in the sea and divers are to undertake a full-scale search of the area where they were found to establish if more remains lie in the depths of the Mediterranean.