The bus crashed into the Alexandre III bridge, a tourist magnet due to its ornate structure and views over the Eiffel Tower and River Seine. The Paris fire service said one of the injured was seriously hurt.
The crash came during a large scale event on the Seine to promote the French capital's bid for the 2024 Olympics, with a floating running track installed across the river just next to the bridge.
A police source said the bus was not travelling along its usual route, having been diverted because of the Olympic event.
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