Police fired tear gas, stun grenades and water cannon in battles with “yellow vest” protesters around the Champs Elysees in Paris on Saturday and clashes erupted in other cities across France in a third weekend of demonstrations against high living costs.

Police said 129 people had been arrested amid concerns that violent far-right and far-left groups were infiltrating the “yellow vests” movement, a spontaneous grassroots rebellion over the struggle of many in France to make ends meet.

For more than two weeks, the “gilets jaunes” (yellow vests) have blocked roads in protests across France, posing one of the largest and most sustained challenges Emmanuel Macron has faced in his 18-month-old presidency.

- Yellow vests converge in Paris to protest high living costs

- Militants hurl projectiles at riot police near Champs Elysees

- Police unleash tear gas, stun grenades, water cannon

- Protesters skirmish with police in other French cities

- Officials fear infiltration by far-left, far-right groups

- Macron says understands anger, but sticking to reforms

In Paris, masked and hooded protesters picked up and hurled crowd barriers and other projectiles in running battles with police around the world famous Champs Elysees boulevard and beyond into other parts of the capital's central tourism districts.

Six policemen and 14 protesters have been injured, Paris police said.

“We are attached to dialogue, but also the respect for the law,” Edouard Philippe told reporters. “I am shocked by the attacks on the symbols of France.”

Several hundred yellow vests, who have no leader and have largely organised themselves online, sat down around the Tomb of the Unknown Soldier under the Arc de Triomphe at the top of the avenue, singing La Marseillaise, France’s national anthem, and chanting, “Macron Resign!”

On the facade of the towering 19th-century arch, protesters scrawled in big black letters: “The yellow vests will triumph”.

After several hours of skirmishes in the morning, police had appeared to clear the area around the Arc, but rioters and peaceful protesters subsequently returned. Clashes in adjacent streets also broke out where barricades were put up, car windows were smashed and at least a dozen vehicles set alight.

Along the Champs Elysees, which was cordoned off, peaceful demonstrators held up a slogan reading, “Macron, stop treating us like idiots!”

BEYOND PARIS, MACRON STANDS FIRM

Macron said on Tuesday he understood the anger felt by voters outside France’s big cities over the squeeze that fuel prices have put on households, but insisted he would not be bounced into changing policy by “thugs”.

Philippe said there were 5,500 protesters in Paris and some 36,000 elsewhere in France. Police unions reported 582 road blockages.

Nantes airport in western France was briefly closed after protesters reached the tarmac and clashes with police broke out in the city centre. In Tarbes in southwestern France and Le Puy-en-Velay in the centre of the country, protesters laid siege to local police stations. Violent clashes also broke out in Charleville Mézières in the northeast.

“What message do the yellow vests want to pass today? That we set France on fire, or find solutions? I find this (violence) absurd,” Jacline Mouraud, a prominent activist within the yellow vests movement, told BFM television.

But a retired yellow-vest protester said: “The government is not listening. Revolution cannot happen without violence.”

The outburst of anger is strongest on the outskirts of smaller provincial towns and villages, and underlines the gap between metropolitan elites and working class voters that has boosted anti-establishment politics across the Western world.

“Mr Macron wrote a book called Revolution. He was prophetic because it is what he has managed to launch, but not the revolution he sought,” Far-left La France Insoumise leader Jean-Luc Melenchon told reporters ahead of a protest in Marseille.

The immediate trigger for the protest wave was the decision of Macron to raise tax on diesel fuel in a move to encourage the driving of less-polluting cars.

The yellow vests, who enjoy widespread public support, get their name from the high-visibility jackets all motorists in France must carry in their vehicles.

The protests caught Macron off-guard just as he was trying to counter a fall in his popularity rating to 30 percent. His unyielding response has exposed him to charges of being out of touch with ordinary people.