The family's Nissan 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.
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.