The family's badly decomposed bodies were discovered inside widower Vallier's white 4x4 vehicle after it was retrieved from a large pond behind his house in southern Kampong Speu province on 14 January.
Vallier and his two sons and two daughters, thought to have been aged from two to nine, had been missing since September. Vallier's Cambodian wife died in childbirth in 2009.
No cause of death has been determined yet for Vallier, 42, and his young children. But the late Frenchman's Cambodian father-in-law Tith Chhuon told the French news agency Vallier had not committed suicide.
"I believe my son-in-law and my grandchildren would not have committed suicide. I believe they were murdered," he said. "I would also like to appeal to authorities and the holy spirits to find justice for them."
Vallier, who according to his relatives worked as a tour guide, is understood to have moved from France to Cambodia around 12 years ago, arriving in Kampong Speu in 2007.