The incident took place shortly before 4pm near the seaside resort town of Deauville (see below).
The family were from the Bas-Rhin department in eastern France, reported French newspaper Ouest France.
The accident took place in Bonneville-sur-Touques, a few kilometers south of Deauville at an “unprotected” railway crossing with no barrier or alarm.
There were no serious injuries are among the 95 train passengers, the local police tweeted.
An AFP journalist who was on the train said it derailed, without overturning. The train was travelling from Lisieux, also in Normandy, and bound for Deauville