The car was pulled out of a pond behind the family's home in Kampong Speu province, near the capital, Phnom Penh, Saturday, Radio France Internationale reported.
The French Embassy alerted Cambodian authorities in November that Laurent Vallier, 42, and his four children, who were between the ages of 2 and 11 years old, had been missing since September.
"Now we are appealing for witnesses who may recognize the clothes and the shoes we found in the car," said Interior Ministry official Chhay Sinarith. "It's most likely the remains belong to the missing French family."
Vallier, who worked as a tour guide, moved from France to Cambodia about 12 years ago, his relatives said.
The parents of Vallier's Cambodian wife, who died in childbirth in 2009, were at the scene and said they believe the family was murdered.
"He would not commit suicide. I know his heart," said Vallier's father-in-law Tith Chuon.
"We don't know if it's a question of robbery or murder," said police official Touch Heang. "Let's leave our team of experts [to] work on it."