The family of five were travelling along the A39 near Dijon in eastern France at about 07:00 local time on Sunday when their car left the road.
The 31-year-old father, who has yet to be named, died alongside the children, believed to be aged four and 12.
His wife and another of their children survived and were taken to hospital with serious injuries, police say.
Witnesses said driving conditions were good and no other vehicles were involved.
They saw the car veer off the road and go through a safety barrier.
Police are trying to determine why the man lost control of the car and are looking into the possibility he fell asleep at the wheel.
A Foreign Office spokeswoman said: "We are providing assistance following a road traffic accident in France, in which three British nationals have sadly died and two others have been hospitalised.
"We are working closely with local authorities and supporting the families at this difficult time."
A British father and two of his children have died in a car crash on a motorway, French police say.