When the French president, Emmanuel Macron, surveyed the damage at the Arc de Triomphe after the worst violence in central Paris for over a decade, street-cleaners had tried to diligently scrub away graffiti saying: “Macron resign.”

They needn’t have bothered because a small crowd gathered to shout it at Macron anyway.

The day of car-burning and violence in Paris and the ongoing gilets jaunes anti-government demonstrations across France are the biggest challenge to the young centrist since he took office 18 months ago.

Macron, 40, has repeatedly said he would never give in to street protests or be intimidated into rolling back what he calls his pro-business project to “transform” France and drag it out of decades of mass-unemployment and slow economic growth.

But he is under serious pressure to listen to and address the concerns of the gilets jaunes – or yellow vests – named after their high-vis fluorescent jackets. Their protests began as a citizens’ stance against green fuel-tax rises but have now morphed into an anti-Macron movement.

It is becoming harder for the French president to present himself on the world stage as a progressive champion who will lead the fight against populism and nationalism if barricades are burning back home in Paris and protestors slam his government as an arrogant elite.

A cleaner is trying to remove a graffiti calling for the resignation of Macron from the Arc de Triomphe. Photograph: Thibault Camus/AP

Macron’s difficulty is that he was taken off guard when the gilets jaunes demonstrations began spontaneously on roads and roundabout blockades across France two weeks ago, with no leaders, trade unions or political parties behind them.

The government failed to anticipate this sporadic, citizens’ anti-tax revolt. And yet sudden uprisings against tax can prove to be a dangerous tipping point – making it very hard to put people’s anger back in the bottle. This is particularly true in a country like France with a high tax-take and a system of high public spending.

When thousands of masked protestors fought running battles with police in Paris on Saturday, torching cars and starting fires on some of Paris’s most expensive streets, the government called them extreme-right and far-left “professional rioters” who had infiltrated the peaceful protests by gilets jaunes.

But it is clear that Macron’s only hope of preventing more violence is to calm the protest movement by answering its concerns — and these are now varied: from dire living standards and unfair taxes to mistrust in the political system and parliament itself.

Crucially, the gilets jaunes have the support of a majority of the French public. Polls show that half of the French people think they will not personally benefit from Macron’s reforms. Many feel his tax policy favours the very rich.

The French president, Emmanuel Macron, flanked by the interior minister Christophe Castaner (R), inspects the aftermath of Saturday’s clashes in Paris. Photograph: Geoffroy van der Hasselt/AFP/Getty Images

This crisis is particularly acute for Macron because the warning sings were already there in last year’s French presidential election that saw him beat the far-right Marine Le Pen. A high level of abstention, a disgust with the political class, a sense of unfairness and inequality at a political elite perceived to be cut off from everyday working people were all present in the election in which Le Pen won 10 million votes. Those feelings have not gone away.

To win the presidency, Macron created his own new grassroots movement based on a promise to “listen” to people and take the nation’s pulse. He styled himself as the nation’s therapist. The new secretary general of Macron’s party, La République En Marche, warned this weekend that “people don’t need psychologists, they need solutions.”

The French government – which has failed to offer clear concrete solutions and is struggling to identify a representative it can talk to from the unconventional gilets jaunes – is under more pressure than ever to give answers to contain the anger on the street.