The protests started in November over fuel taxes and the high cost of living and morphed into a more general revolt against President Emmanuel Macron and a government they see as out of touch.
Nicolas Mollier, an organiser, said the protesters hoped to bring their case to the attention of a UN official.
"France must be held accountable," he told Reuters Television. "Today, there are victims who have lost an eye, victims who have had their hands blown away or their feet."
"Yellow vest" actions have at times been marred by violence, and according to a survey published last week by pollster Elabe, 56 percent of French people want the weekly protests to end.
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