The family's car hit a safety barrier on the A39 motorway around 80 kilometres (50 miles) south of the city of Dijon, jumped over an embankment and hit a bridge pillar before falling back onto the road, according to initial investigations.
Images from the scene showed the shattered remains of the car lying on its side on the road, with belongings and debris strewn around.
The 31-year-old father and two children aged four and 12 were killed on the spot, emergency services said.
A third child was airlifted to hospital with serious injuries, while the mother escaped with only minor injuries.
A firefighter at the scene told France 3 television that when crews arrived, the father was still alive, trapped in the wreckage, but died soon after being freed.
The cause of the accident, which happened soon after 7am, is still under investigation.
But a police officer told France 3 the father, who was driving, may have fallen asleep at the wheel or been distracted by something.
The family's surname was given by the authorities as Crompton, but no further details were immediately available.
Some unconfirmed reports said the family had been travelling from Italy.