The Ministry of the Interior said there were 27,900 protesters across France, 9000 of them in Paris. Turnout appeared to be slightly less than last week (31,100).
Yellow Vest protest organisers said they estimated 100,000 people turned out across France.
There were scuffles between police and protesters in the afternoon, after hours of calm, as police used anti-riot grenades and tear gas to disperse marchers as they made their way towards Place de la Republique in eastern Paris, the culmination of the march.
Police said they intercepted 227 people and carried out 20,500 spot checks throughout the course of the day.
Some protesters threw rocks and bottles and set trashcans on fire. Several people have been injured, according to journalists on the scene.
President Emmanuel Macron was due to unveil policies meant to quell the Yellow Vest protests on Monday, but he cancelled the speech due to the fire at Notre-Dame. He is now set to make his announcements next Thursday.
Macron hits lowest score so far in new opinion poll
In a new poll released by Opinionway on Saturday, only 27 percent of French peopls interviewed said they were satisfied with Macron's actions. That's five percent less compared to March, and the lowest score registered since Macron's election. 40 percent said they were very unhappy with the President's policies.
In terms of the Yellow Vest protests, 48 percent said they supported the movement and soutenir, while 48 percent said they no longer supported the movement.
Earlier this month, President Macron signed into law legislation that gave security forces greater powers at demonstrations but which opponents claimed violated civil liberties.
One measure banned protestors from covering their faces, but France's Constitutional Council, its highest constitutional authority, refused to give its green light to one of the most contentious parts of the legislation.
It would also have given the authorities the power to ban from demonstrations any individual "posing a particularly serious threat to public order".
The "yellow vest" movement is demanding changes to the government's social and fiscal policies.