He has vowed that those responsible for the violence and the damages will pay for their actions.
Numerous provisions, including expanded ID checks and restrictions on public gatherings, were incorporated into a new security law pushed through by President Emmanuel Macron when the emergency measures were lifted past year.
The violence has caused deep concern in the French business community which claims it has already lost billions of euros and is set to attend a meeting at the Economy ministry on Monday.
Demonstrators are also furious about President Emmanuel Macron's leadership, and in particular, his Government's broader economic policies.
Since the yellow jacket movement kicked off on November 17, two people have been killed and hundreds injured in clashes or accidents stemming from the protests.
More than 400 people were arrested and at least 130 injured over the weekend in battles between police and the so-called gilet jaune (yellow vest) protesters.
Macron has borne the brunt of the demonstrators' anger instead of OPEC for reducing oil production, or the United States for imposing tariffs on Iran, which crippled oil exports. Dozens of cars were set on fire and shops looted, with police firing tear gas and water cannons.
They're decentralized: The protests are chiefly organized using social media rather than being led by any formal, organized parties, unions, or other groups.
An assault rifle was stolen from a police vehicle, a source told AFP, though it was unclear if it was loaded.
One person was in a critical condition after protesters pulled down one of the huge iron gates of the Tuileries garden by the Louvre, crushing several people.
"We want our dignity back and we want to be able to live from our work, which is absolutely not the case today", Mr Jason Herbert said after walking out of talks with Prime Minister Philippe on Friday.
After he returned to Paris Sunday morning, he went straight to the Arc de Triomphe and then held a crisis meeting with top ministers.
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"I will never accept violence", Macron said.
Almost 190 fires were put out and six buildings set alight, the interior ministry said. 412 people were arrested, with 378 of them still in custody at the time of writing.
Clashes between police and demonstrators wearing the high-visibility yellow vests broke out soon after crowds began gathering near the Arc de Triomphe on Dec 1, 2018.
Reporting from Paris, Al Jazeera's David Chater said that the attacks on the monument were carried out by a small minority of the protesters, but the damage to the landmark has touched a nerve in the French government.
Interior Minister Christophe Castaner denounced what he called the "professionals of disorder" and destruction who had organised the violence.
"That's why his popularity is at 26 percent, and we see riots occurring in such a way that he may have to declare a state of emergency", he said. "I am prepared to examine everything".
"You always have some idiots who come to fight, but they don't represent us at all".
The Champs-Elysees itself was on lockdown, its glittering Christmas decorations standing in stark contrast to boarded-up storefronts and throngs of riot police manning barricades and water cannon.
While the majority of protesters are frustrated citizens concerned about the cost of living, the anger also gives cover to those who just like to smash things up.
"He has to come down off his pedestal", she said under cold rain on the Champs-Elysees. Since he took office 18 months ago, the French president has seen public pushback on nearly every one of his reforms, especially liberalizing the labor market.
The protesters, upset with increasing taxes and the high cost of living, rioted Saturday in one of the city's most popular tourist areas, according to published reports. Over the past three weeks, protesters have been setting up road blockades across the country and their movement has garnered wide public support.