Paris:  Paris' Eiffel Tower will close on Saturday over fears of fresh violence during nationwide protests against President Emmanuel Macron, as police urged shops and restaurants on the Champs-Elysees to shut their doors too.

Around a dozen museums across the capital have also said they will remain closed on Saturday after vandalism and clashes between protesters and police last week rocked France.

The announcements came as around 200 high schools across the country remained blocked or disrupted by students protesting a raft of education overhauls, on a fourth day of action called to coincide with the anti-government demonstrations.

An interior ministry official told AFP earlier that authorities were bracing for "significant violence" on Saturday, based on indications that protesters on both the far right and far left are planning to converge on the capital.

Prime Minister Edouard Philippe told senators Thursday that "exceptional measures" would be taken to avoid the daylong street battles seen last weekend, with 65,000 police deployed across the country.

Shops along the Champs-Elysees as well as popular shopping streets near the iconic avenue were told to keep their doors closed, protect exposed windows and remove any outdoor furniture including tables and chairs, according to the police notices seen by AFP.

The move is likely to cost businesses thousands of euros in lost revenue as tourists and locals alike stay clear during a second holiday weekend in a row.

The Eiffel Tower said it would stay shut Saturday, and both the Garnier and Bastille opera houses have cancelled performances scheduled for Saturday.

Shops are also expected to close in other cities, with officials in Bordeaux, southwest France, already warning that museums, libraries and theatres will remain shut.

A Paris Saint-Germain football game against Montpellier scheduled for Saturday has also been postponed after a request by Paris police, and some schools near the Champs-Elysees have called off Saturday classes.

Two of Paris's main attractions, the Louvre and Orsay museums, are still weighing whether or not to close.  The "yellow vest" protests began on November 17 in opposition to rising fuel taxes, but they have since ballooned into a broad challenge to Macron's pro-business agenda and style of governing.

The government announced Wednesday it would cancel planned increases in fuel tax due to take effect in January in a bid to appease the mostly low-income protesters from small-town and rural France.

But the concession failed to quell the anger behind a movement which has retained broad public support, with an opinion poll this week showing 72 percent backed the protests despite last weekend's violence.

The "yellow vests" have also spurred other protests, in particular students demanding an end to testing overhauls and stricter university entrance requirements.

Dozens of people wearing face masks threw Molotov cocktails, torched rubbish bins and clashed with police outside schools in several cities Thursday ahead of a call for nationwide demonstrations on Friday.

"We're the ones who are going to eventually have to pay higher fuel prices," said Ines, one of around 150 high school students demonstrating in the southern Paris suburb of Cachan.

Farmers have also called for demonstrations every day next week, while two truck driver unions plan an indefinite sympathy strike from Sunday night.

Meanwhile yellow-vest blockades at fuel depots have caused shortages in Brittany, Normandy, and southeast regions of France.

Political leaders from across the spectrum have appealed for calm, after four people died in accidents during protests and hundreds have been injured.

On Thursday a yellow-vest representative, Benjamin Cauchy, called on Macron to meet a  delegation of protesters Friday to help defuse a situation that he said had brought the country "to the brink of insurrection and civil war."

"We're asking him to meet us to negotiate on spending power, which is what underpins all this anger," Cauchy told AFP.

Macron, whose approval ratings are down to just 23 percent, has not commented publicly since Saturday on the deepest crisis of his presidency so far.

But members of his government have signalled they are ready to make further concessions to avoid new violence after the U-turn on fuel tax increases.

But Macron's office said he told ministers he would stick to his decision to cut a "fortune tax" on high-earners, which the former investment banker abolished last year.

Restoring the wealth tax has become one of the core demands of the "yellow vests," alongside the fuel tax rollback and an increase in the minimum wage.