Groups of defiant "yellow vest" demonstrators faced off with thousands of police around France today, but their numbers were lower on what was the fifth weekend of protests for the anti-government movement.

President Emmanuel Macron, facing the biggest crisis of his presidency, announced a series of concessions on Monday to defuse the explosive "yellow vest" crisis, which swelled up from rural and small-town France last month.

He was hoping that the package of tax and minimum wage measures for low-income workers, coupled with bitter winter weather this weekend, would help bring calm to the country after more than month of clashes and disruption.

France was also hit by a fresh terror attack on Tuesday night when a gunman opened fire at a Christmas market in Strasbourg, leading the government to urge people to stay at home to spare the country's stretched security forces.

At midday today, an estimated 33,500 people had taken to the streets, according to figures from the interior ministry, around half the level at the same time last weekend.

"It's a bit disappointing. We expected there to be more people, but the movement won't end," Francis Nicolas, a 49-year-old labourer, said in the southeastern city of Lyon.

There were only a few hundred people dressed in the florescent yellow high-visibility jackets in front of the city's main court building, compared with 7,000-10,000 last weekend.

In Paris, police outnumbered protesters by nearly 4-1 in the early afternoon, with around 2,200 protesters counted on the streets of the capital by local authorities compared with 10,000 last week.

Security forces played a game of cat-and-mouse with groups of them as they roamed around shouting slogans through the centre of Paris, much of which was cordoned off from traffic.

There were isolated incidents of tear gas being fired, but a fraction of the amount used on previous weekends when graffiti was daubed on the Arc de Triomphe in scenes that shocked France.

Until this week, a clear majority of French people had backed the protests, which sprung up initially over high taxes before snowballing into a wider opposition to President Macron's pro-business agenda and style of governing.

But two polls published on Tuesday - in the wake of the government’s concessions - suggested the country was now broadly 50-50 on whether the protests should continue.

Outside Paris, groups of "yellow vests" occupied roundabouts to slow down traffic, and there were major delays on the motorways in southern France as well as on the A16 near Calais in the north.

Authorities reported the seventh death linked to the demonstrations in a fatal road accident on Friday evening near the France-Belgium border.

More than 1,400 people have been injured since the protests began on 17 November.