The bus, operated by German company Flixbus, was en route to London from Paris on Sunday when it skidded off a highway in northern France and flipped on its side.
Local officials said 33 people were injured, four of them seriously. They have been taken to nearby hospitals.
The accident took place on the A1 motorway near the city of Amiens. The Courrier Picard newspaper reported that the road was wet when the bus swerved on a curve, crashed into a barrier and then overturned.
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According to authorities, most of the passengers on board were foreigners from countries including the United States, Spain, Australia, the Netherlands, Romania, Russia and Britain. Thirteen of the injured passengers were French.
Flixbus said in a statement that it regretted the accident, adding that the company was working with authorities to determine what had happened. It said the bus was operated by a local partner under the Flixbus brand.
nm/jlw (AFP, dpa)