The coach smashed through the safety barrier on the side of the road and hurtled 40m onto the banks of the river Romanche below.
It burst into flames as it came to rest beside the river and was gutted by fire.
Local people tried to put out the blaze with buckets of water.
A large number of rescue workers arrived after the local governor's office activated an emergency plan.
The injured were shuttled to hospitals by ambulance and helicopter.
Divers searched for victims who may have been thrown into the river.
Most of those on board the bus were elderly and came from the Szczecin region of northeast Poland, officials in Warsaw said.
They were on a tour of European Roman Catholic shrines and had spent the night at Notre Dame de la Salette.
Robert Szaniawski, a Polish foreign ministry spokesman, said the ministry had set up a telephone hotline for families.
Szaniawski said: "They left Poland on July 10 and were on their way back."
The office of Francois Fillon, the French prime minister, said he was due to visit the scene during the day.
The RN85 road from Gap to Grenoble has been the scene of many accidents over the years.
Three coach crashes occured at exactly the same spot in the 1970s causing 77 deaths.
Investigators were likely to concentrate on the condition of the Polish coach.
The descent is only authorised for use by buses if they are equipped with electronic braking.