In the worst incident, a female protester died after a driver surrounded by demonstrators panicked and accelerated.
The "yellow vests" movement, named for the high-visibility jackets worn by supporters, erupted on social media last month with calls for blockades of roads and highways.
An investigation into the death was opened. She accidentally struck and killed a woman in her 60s, the interior ministry said.
"I really want people not to let themselves become submerged by anger", Alexandrine Mazet told RTL radio.
"This government hasn't understood the anger of the French", Socialist Party secretary general Olivier Faure said in a statement Wednesday. The young woman appeared later on BFMTV still wearing her yellow vest.
The nationwide protest was unusual due to its grassroots origins.
Opposition parties and labour unions have voiced support for the demonstration but most have not joined, wary of being seen alongside officials from the National Rally and other far-right groups. Police used tear gas to stop demonstrators on the Champs-Elysees.
Castaner said a handful of other injuries had been reported in other areas, including a police officer in the southern city of Grasse outside Nice, by drivers trying to force a way through the blockades.More news: Model, actress Kim Porter passes away at 47
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Recently they surged after petrol prices went up and now they have evolved into a wider movement against President Emmanuel Macron's government.
While Macron, whose popularity is hovering around a dismal 30 per cent, said he regretted that he was not able to reconcile his government with the people, he has refused to back down, saying, "We have to tax fossil fuels more in order to fund our investments in renewables". A "carbon trajectory" calls for continued increases. The tax on gasoline is to increase 4 euro cents.
Many drivers see this as emblematic of a presidency they view as disconnected from day-to-day economic difficulties and serving the rich.
The tax hike is so widely unpopular, that even 54 per cent of those who voted for Macron support the movement, with 73 per cent of Frenchmen of all political persuasions supporting the Yellow Vests.
Robert Tichit, 67, a retiree, referred to the president as "King Macron".
"We work like slaves and at some point enough is enough".
"There are many young people among us because we can't make ends meet anymore", said Emilie, a 27-year old temporary sales manager in Cavaillon in the south of the country.
In Paris, several hundred protesters yelling "Macron resign!" and singing La Marseillaise massed on the Champs-Elysees and the Place de la Concorde, hoping to march toward the Elysee Palace, Macron's official residence.