Still, it was a rare accident for the popular sightseeing boats - known as bateaux mouches - that ply the river day and night.
"I was facing the other way," said Audrey Haughton, from Oxfordshire. "And then, nothing, black. I just felt knocked out. I hit my head on the railing."
Mrs Haughton's husband was carried out by paramedics on a bright orange body splint - apparently the one person seriously injured. "He was talking and then he collapsed," she told reporters. "I don't know any more."
Bernard Schmitt, from Alsace, was there with his son. "There were people who went over the tops of the seats," he said.
The accident happened just before noon, in the heart of Paris. The boat, the Parisis, is owned by the Vedettes du Pont Neuf company, one of about a half-dozen companies that run tourist boats along the river. The company's director, Eric Levavasseur, said the problem happened when the boat was about to pass under the Pont Royal.
Due to an electronic glitch, the boat struck an arch of the bridge before the captain had time to correct the move, he said. Then, he added, the boat went back to its course and made its way back to its dock near the Pont Neuf.
The boat, with a capacity for 100 people, was carrying about 70 tourists of different nationalities.
Most of the injured appeared to have suffered bruises, but were not seriously hurt. A woman in her 60s hurt her neck, and had to be put in a neck brace.
Sixteen people were sent to nearby hospitals, police said. About 50 firemen were on hand to help with the rescue efforts.
"Obviously people were panicked by the shock," said a river fire brigade spokesman. "This was a pleasant tourist cruise, and you don't exactly expect something like this."