France's Yellow Vest movement took to the streets en masse on Saturday for the fourth week running, even though the fuel tax rises that sparked their protests have been cancelled.

But President Emmanuel Macron's government was able to claim a partial victory, as a major police mobilization helped avoid the running battles that marred protests in Paris last week.

With official figures showing 125,000 protesters across France, Prime Minister Edouard Philippe said it was time for dialogue, "to knit our national unity back together."

Macron, who has been silent since last week's violent scenes in the capital, would soon propose measures "to nurture this dialogue," the prime minister said.

The day's calm was only relative: Police clashed with protesters in several areas of Paris, often resorting to tear gas and water cannon. Local media reported violent clashes in the south-western city of Bordeaux.

Security forces arrested 1,385 people across France, with 985 held for questioning, Interior Minister Christophe Castaner said.

Some 118 protesters were injured, mostly in traffic accidents, Castaner said, compared to 220 last week. Only 17 members of security forces were injured, down from 284 last Saturday.

Gendarmerie police said they had checked more than 5,000 people on the roads around the capital in the morning, confiscating potential weapons and protective equipment.

From the early morning, police let hundreds of the protesters, clad in the fluorescent yellow safety bibs that have become the movement's symbol, filter onto the Champs-Elysees after careful searches.

Better preparations by authorities paid off in other ways too. 

On the Grands Boulevards running through the north of the capital, roadworks barriers and metal street furniture had been taken away, leaving less material than last week for radical leftist protesters to build barricades with.

The French capital's Right Bank was unusually quiet for a Saturday, with few signs of the usual motor traffic or crowds of tourists.

Many shops and restaurants were boarded up, fearing a repeat of last week's vandalism.

The relative calm seemed to owe more to the revised police tactics than to the government's decision on Wednesday to cancel the petrol and diesel tax rises that had been due to take effect next year.

The number of protesters was only marginally down on last week. In Paris, at 10,000 according to Castaner, it was up on last week's official estimate of 5,500.

Yellow Vest protesters in the capital seemed unimpressed by the government's concessions, as chants of "Macron, resign," rang out.

"You know, that's all just for show," one Yellow Vest protester, who was joining in on-off blockades of traffic on the Place de la Bastille, told dpa when asked about the government climbdown.

Jeremy, 36, a local government official from a region near Paris, said people felt that their tax money was "being robbed."

"When you see how those who govern us live!", he added. "We want some justice too, a fairer distribution of wealth."

With the far right and radical left both trying to ride the movement's bandwagon in France, foreign voices joined the fray too.

Steve Bannon, the former strategist of US President Donald Trump, said at an event on Saturday in Brussels that the Yellow Vests in France are the "exact same type of people" that voted for Trump and for Brexit.

Left-wing Canadian author and anti-globalization icon Naomi Klein meanwhile wrote on Twitter that the protests showed the need for a new approach to climate policy. "Neo-liberal" pro-business climate action was seen as "a class war, because it is," Klein tweeted.

The protests have spilled over from France into Belgium and the Netherlands.

On Saturday, hundreds of people took to the streets in the Netherlands demanding that Dutch Prime Minister Mark Rutte step down and their country exit the EU, among other things.

In Brussels, about 400 people were arrested at the protests, with 1,000 people taking part according to police.