The demonstrations spiraled into clashes with the police and a protest against the country's leadership, whom protestors accuse of ineffective government and taking insufficient measures to fight poverty.
About 55,000 gilets jaunes (yellow vests) joined the protests on Saturday, with more than 5,000 in Paris.
Another video features a Porsche in a parking lot with its windows shattered and pink smoke coming out of it. Witnesses said he lost four fingers after trying to knock away a concussion grenade.
As scuffles broke out in front of the National Assembly and French police responded with tear gas, paramedics huddled around the injured protester at the National Assembly gates, providing emergency treatment and stopping bystanders from getting too close. Representatives for the yellow vest movement dispute that claim, according to the BBC.
Italian Deputy Prime Minister Luigi Di Maio said French President Emmanuel Macron saw his meeting with Yellow Vests protesters as "lese-majeste", defending a controversial move that prompted Paris to recall the French ambassador from Rome and sparked a crisis in bilateral ties.
Volunteer medics at the National Assembly told AFP that a man had had his hand ripped off during the clashes between police and protesters.
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Police said 31 demonstrators had been arrested in the unrest.
"But between the French people and the Italian people there is no problem".
In December, Mr Macron said he was "partly responsible" for an "insufficient response" to the protests that have rocked the country every Saturday. That was down from the previous week, when official figures put the number at 58,600, 10,500 in the capital city.
'A right-wing group of yellow vests attacked a left-wing one, and the result was carnage, ' said a protester who witnessed the violence.
Protests also took place in other French cities, including Marseille, Montpellier, Bordeaux and Toulouse, the BBC noted.