A boy aged 12 and a girl of 15 died when the driver lost control in snowy conditions and the bus overturned near Montflovin in the department of Doubs.
The driver and three children were slightly hurt in the crash as the bus travelled between Monteau and Pontarlier at about 07:40 (06:40 GMT).
They were evacuated to Pontarlier and the road was closed.
Officials said that a snowplough had cleared the road during the night and it had been treated with salt, although there would have been some snow on the surface by morning.
The cause of the accident is unclear although a collision with another vehicle has been ruled out.
Some reports suggested the bus had been travelling too fast for the conditions.
The driver had been taking 33 children to Lucie-Aubrac school near Pontarlier.
He was among those taken to hospital but local prosecutors said he would be investigated as part of a manslaughter inquiry.
Prime Minister Manuel Valls wrote on Twitter of his immense sadness and full support for the families of the two children who died.
Two children have been killed and seven more people have been injured in a school bus crash in eastern France.