Some scuffles broke out on Saturday in central Paris between protesters and police after nearly 4,000 people came out in the capital, raising anti-government slogans and blocking traffic.
Riot police fired tear gas and sprayed the protesters to disperse them. Police said they arrested more than 100 people, Reuters news agency reported, citing a Paris police official.
About 8,000 police and 14 armoured vehicles were deployed in Paris after similar protests in recent weekends turned violent.
The Interior Minister said around 69,000 police were active on Saturday with a reinforced presence in Toulouse, Bordeaux and Saint-Etienne.
Official figures said 66,000 protesters had been counted in France by 17:00 GMT, compared to 126,000 at the same time a week before.
President Macron, facing the biggest crisis of his presidency, announced a series of concessions on Monday to defuse the "yellow vest" movement, which sprang up in rural and small-town France last month.
He was hopeful that the package of tax and minimum wage measures, coupled with bitter winter weather, will help end a month of violent clashes and disruptions.
"Last time, we were here for taxes," a 28-year-old Jeremy told the AFP news agency as he joined others gathering in freezing cold on the Champs-Elysees.
"This is for the institutions: we want more direct democracy," he said, adding that people needed to "shout to make themselves heard".