French media say police could in future cordon off the famous Champs-Elysées avenue. Chic boutiques and a restaurant were vandalised there on Saturday.
During the clashes, a policeman was filmed apparently stuffing Paris Saint-Germain football shirts into a bag.
Police are probing that incident.
A PSG store was among those damaged during Saturday's unrest, which involved an estimated 10,000 protesters.
The video, tweeted by journalist Rémy Buisine, veers away from the policeman dramatically seconds after he was filmed, and Buisine is heard shouting: "Why are you hitting me like that? What right have you to hit my phone?"
He also asks the police why their ID numbers are not visible.
One is heard replying: "You're liars."
The "yellow vests" began weekly protests across France four months ago, initially because of fuel tax rises. The movement escalated into a broader revolt against perceived elitism, for which activists blame President Emmanuel Macron.
The famous Fouquet's restaurant - a haunt of some previous French presidents - was badly damaged in Saturday's clashes.
Rioters also vandalised a Boss menswear store and the luxury Longchamp handbag store.
Later Prime Minister Edouard Philippe admitted there had been security "flaws" which would have to be addressed.
Mr Macron cut short a skiing holiday and vowed "tough" action in response.
"Now that's the end. I demand that such scenes must not be repeated, especially on that avenue," he said.
Police used water cannon and tear gas to disperse the protesters. More than 120 people were arrested.
Protesters threw cobblestones at police at the Arc de Triomphe war memorial.
The "gilets jaunes" mobilisation was bigger than for similar demonstrations in recent weeks.
Some 32,300 in total took to the streets throughout France, according to the interior ministry.
Business executives are to hold "crisis" talks with Economy Minister Bruno Le Maire on Monday, Le Figaro daily reports.
The Paris Ile-de-France Chamber of Commerce says it wants an emergency plan, and that 91 businesses were hit on Saturday, nearly all of them suffering serious damage.
Mr Macron offered concessions to the protesters after the movement swept the nation - including €10bn (£8.5bn; $11bn) designed to boost the incomes of the poorest workers and pensioners. But they failed to quell the discontent.
For the past month he has toured France, listening to local mayors and citizens as part of his "grand débat" - a big national debate.