The crash occurred at 7.40am on Wednesday in Montflovin in the Doubs département of eastern France.
There were reportedly 33 children on board the bus, two of whom were killed and at least four of whom sustained minor injuries.
Both pupils who died were 15 years old, reported L'Est Republican newspaper.
The bus driver was reportedly among the injured.
The paper reported that the bus driver lost control on a snow-covered road, careering onto the ice and snow and sliding up to fifty metres.
Photos from the scene show the bus on its side with the windshield missing.
Conflicting reports have suggested that the bus collided with another smaller vehicle, although exactly how the crash occurred remains unconfirmed.
The bus crashed on a road near the Swiss border. Photo: GoogleMaps
The father of a child inside the bus suggested that speed was a factor.