Ultra-right groups want to tap into the widespread anger against President Macron to help overthrow the “system”, reports The Times.
The paper said it had seen brochures saying such groups are keen to exploit the popular anger against the French leader.
Machine operator Olivier Bruneau, 41, said he was seeing the start of a new uprising.
Drawing parallels with the Revolution, he added: “Imagine that this is a new 1789. That’s our reference point.”
Meanwhile, Pascal Lercier, 62, a retired teacher, said: “The people have woken up.”
The continued anger comes despite Emmanuel Macron suspending France’s controversial rise in fuel taxes in a humiliating u-turn following weeks of violent protests.
His climb-down was confirmed by his prime minister, Edouard Philippe, who also said planned hikes for electricity and gas prices had been put on hold.
Philippe said the tax increase would be suspended for six months, adding: “No tax is worth putting the nation’s unity in danger.”
But Yellow Vest fuel protesters who have turned Paris and other cities into war zones over the past two weekends said their protests would continue as they campaign for more tax reductions.
“It’s a first step, but we don’t want crumbs,” said Benjamin Cauchy, a spokesman for the movement, which takes its name from the high visibility yellow jackets that all motorists are expected to own in France.
He said: “Demonstrations will continue as we fight for further demands.”
Cauchy added that he had received “30 death threats” after pleading for his movement to halt its campaign of violence.
His comments come as video footage has been released showing French police beating up protesters in a fast food restaurant.
Yellow Vest demonstrators wanted to enter the premises to take cover from teargas being used by French riot police.
With the restaurant closed during the fracas, under the pressure of campaigners, the glass entrance door was broken, and they rushed inside.
Cops followed them in, and they were beaten with batons.
There were more than 400 arrests in Paris at the weekend, as thousands fought running battles with riot police.
Right-wing thugs and masked anarchists joined the Yellow Vest protesters last week – vandalising Parisian buildings such as the Arc de Triomphe and torching cars.
Looters stole thousands of pounds worth of goods from high-end boutiques around the Champs Elysee, and from bars and chemists.
Previously, Macron had insisted fuel prices had to rise in line with green initiatives made necessary by the Paris Climate Change agreement.
But following two weekends of violence, French police admitted they “can’t cope” and called on the government to send in the army ahead of a third weekend of riots.
Paris saw the worst of the unrest which has been compared to the infamous protests in May 1968 – when a workers’ strike paralysed the country for seven weeks and turned the capital into a warzone.
In the second week of violence, the anti-government rioters, who threw hammers and steel bolts at officers, said their movement was “the start of a revolution”.
Yves Lefebvre, a member of the Unité SGP police union, told France Info radio that security forces at the weekend were exhausted by the carnage.
He said: “The (officers) don’t want to remain as the last rampart against insurrection. We can’t take it – I call on the president to face up to his responsibilities.”
But despite the government u-turn, the carnage could continue regardless.
Extremist brochures obtained by The Times shows that ultra-right wing groups are seeking to turn the unrest into a full-blown revolution.
The estimated 300 ultra-right militants who took part in Saturday’s violent demonstrations in Paris were reportedly well-organised and mostly avoided arrest.
The “yellow vest” movement, named after the high-visibility jackets of lorry drivers,said that they would return to the capital next weekend.
And there have been calls online to block roads and oil refineries around the country while other demonstrators plan to march on the Élysée Palace.
What are the France fuel protests?
In France, the cost of diesel has increased by around 23 per cent in the last year.
It is the most commonly used fuel in French cars, but motorists are now paying €1.51 (£1.32) per litre when they fill up.
It’s the highest price for diesel in France since the early 2000s.
World oil prices did rise before falling back again but the Macron government raised its hydrocarbon tax this year by 7.6 cents per litre on diesel and 3.9 cents on petrol, as part of a campaign for cleaner cars and fuel.
The decision to impose a further increase of 6.5 cents on diesel and 2.9 cents on petrol on 1 January 2019 was seen as the final straw for drivers.
In backing down from his tax hike, Macron joins a long list of French presidents who have bowed down to rioters.
Conservative leaders Jacques Chirac and Nicolas Sarkozy were notorious for withdrawing unpopular policies because of street disturbances, as were their Socialist counterparts.
Yesterday, footage emerged showing a cowering protester being battered by baton-wielding police who chased him down a Parisian street during the weekend’s violence.
In the disturbing video, the unnamed man is chased by cops in Rue de Berri, a half-mile from the Arc de Triomphe, before being thrown to the ground by one officer.
Another six policemen then join him in kicking the demonstrator and striking him with batons.
It is not known what sparked the beating which was filmed by an onlooker from a window across the street.
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