Prosecutors in Bourg-en-Bresse are leading the inquiry. Further details on the route and the sequence of the crash have not been made public.
The side of the bus was torn off. People who had been sitting on that side were seriously injured, according to descriptions of the wreck.
Emergency crews treated the wounded at the scene. Survivors were taken to the town hall while the investigation continued.
Addressing conditions at the time of the crash, the mayor told Le Figaro"there was a bit of fog, the road was wet"but there were"no major difficulties".
The bus was carrying 43 passengers, including 15 children, the Bourg-en-Bresse prosecutor's office said. Authorities have not released the names of the dead or a full count of the injured. They have not said what caused the vehicle to leave the road.
Local mayor Cristin told BFM TV:"I arrived minutes after the accident and people were in shock.".
The crash involved a large group of passengers, many of them children, on a wet road in fog. Officials said the weather did not present major difficulties. A child and a young adult were killed when a bus crashed in eastern France, local authorities said. Several other people were injured.
The town hall was opened to provide shelter and to coordinate with emergency services, the mayor said.