Olivier Jannequin, 41, died on August 18 minutes after the speedboat hit him in the sea off Koh Phi Phi.
The boat did not stop after the incident and none of the hundreds of holiday-makers on the beach helped a friend of Jannequin -- who had been swimming near him -- bring his body to shore, La Nouvelle Republique newspaper reported.
Prosecutors in the western French city of Rennes, where Jannequin lived, are examining the family's suit, which does not specify a defendant, officials said.
La Nouvelle Republique said Thai police had so far failed to find the driver of the boat.