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French security forces fired tear gas and flash-bang ammunition at protesters during a march through central Paris as several thousand supporters of the yellow vest movement kept up pressure on President Emmanuel Macron with the first action of 2019.

A river boat restaurant moored below the clashes on the Left Bank of the Seine River caught fire, while smoke and tear gas wafted above the Orsay Museum and the gold dome of the French Academy as riot police moved in when protesters deviated from an officially approved path.

Police boats patrolled the river while beyond the Seine, motorcycles and a car were set on fire on the Boulevard Saint Germain, a main Left Bank thoroughfare.

Riot police and firefighters moved in, and barricades mounted in the middle of the wide street also glowed in flames.

The march on the eighth consecutive Saturday of yellow vest protests had been declared in advance and approved, in contrast to some illegal December demonstrations that degenerated into vandalism, looting and chaos.

The atmosphere was mostly calm, but turned when some protesters tried to cross the river on a pedestrian bridge not on the official route from City Hall to the National Assembly.

Police used clubs and tear gas, then held the bridge in a stand-off while violence broke out.

Further confrontations between police and protesters took place in other cities around France, with tear gas fired in Bordeaux and in Rouen, Normandy.

No official figures have been issued for the number of protesters who turned out around France or in Paris, though one police estimate put the marchers in the capital at 3,500.

Protesters were looking to breathe new life into the yellow vest movement as numbers of participants has fallen since the first Saturday protest in mid-November.

They reiterated their call for Macron, denounced as the president of the rich, to resign

Government spokesman Benjamin Griveaux said those still protesting "want insurrection".

He called on the French to express their views during a "national debate" organised in the coming weeks in all regions, rather than by taking to the streets.

The yellow vest movement was launched to express anger over fuel tax hikes affecting working people who commute by car, but grew to encompass broader anger over Macron's economic policies, deemed to favour the rich.

Meanwhile, in London, a 13-year-old girl was among four arrested as demonstrators took to London's Westminster Bridge for a pro-Brexit "yellow vests" demonstration.