Assembling in front of the Paris main demonstration over 1,000 youths with black jackets and face masks took to the head of the march shouting slogans such as "Rise up, Paris" and "Everyone hates the police".
Some carried placards with the Anarchist symbol and banners with references to the far left "black bloc" protesters who regularly clash with police at international summits.
Along the route of the march they looted and set fire to a McDonald's restaurant and also torched a car, a mechanical digger and a scooter. The police used tear gas and a water cannon to try disperse them.
At least two people were arrested over the unrest, which comes at a time of heightened tensions over President Emmanuel Macron's reform of the public sector.
"Macron makes us mad," read a banner held by one masked demonstrator.
Interior Minister Gerard Collomb condemned the violence.
"Everything is being done to end this serious disturbance to the peace an find those responsible for these unspeakable acts," he tweeted.
No common cause
The 2018 march wa very different from that of May 1st, 2002, when unions managed to rally protesters to a common cause when 1.3 million people demonstrated following a joint call from French trade unions to "stop" Jean-Marie Le Pen. No such a common cause exits at the moment.
Even last year last year, in the run up to the presidential elections, the unions failed to agree on a common position in respect of the far right’s Marine Le Pen, who had made her way into the second round of voting in the presidential election.
"We must show unity against a government that hits hard," Martinez said on Tuesday morning on the national news station BFM TV. Asked about unity he said: "We are working on it," stressing that "all the social conquests in this country [France] were obtained when the unions were united".
Force Ouvrière's new leader, Pascal Pavageau, admitted on the French news radio station, franceinfo, that "the confederations [unions] have not, perhaps, been sufficiently seen and united" to make a "common diagnosis of what is happening".
In all, the CGT called for 240 demonstrations or rallies across the country, under an umbrella call-to-action that goes "Against the questioning of the social progress, [against] the selection for university. For the social progress, the peace, the international solidarity!"
The Paris 1st of May 1st, organized with a number of other unions – the FO, FSU, Solidaires and Unef, left Place de la Bastille in the east of Paris in the early afternoon and headed south in the direction Place d'Italie.
In the regions, Eric Beynel, spokesperson for the union Solidaires, said he expected "greater union unity" in some cities, with the presence of the CFDT on the marches.
In the capital, the had previously warned against the infiltration of the march by "extremist groups" looking to turn the event into "a great revolutionary meeting".
Last year, nearly 142,000 people protested in Paris according to the police, during which six policemen were injured, one seriously by a Molotov cocktail.