According to the French Interior Ministry, about 440,000 people took part in national protests.
Of them, 110,000 protesters marched into the capital city of Paris.
The celebration, organised by trade unions, was earlier displaced by authorities on the outskirts of the city.
The CGT union confederation, according to media reports, spoke of some 800,000 participants.
While no major incidents were initially reported, late afternoon and in the evening the first riots broke out.
Images from Paris showed tear gas and the use of water under pressure as TV broadcasts heard explosions and loud noises.
Police clash in several cities
Tear gas was also used in cities like Lyons, Bordeaux, and Marseilles. Media reported clashes between protesters and rule forces.
In the town of Nantes, northwest of France, injuries and looting were reported at a store, relevant Prefectures reported.
Security forces arrested six people. Reports indicate that cases of looting were observed in other areas of the country.
In Toulouse, one person was seriously injured in hand during clashes with police, media reported.
French Interior Minister Laurent Nuñez stated in the early afternoon that by 1: 00 p.m., police had arrested 135 people.
A number of dangerous objects were seized during raids in the Paris region.
Nuñez also stressed that authorities had established a much larger police presence. According to him, about 70,000 effective police officers were engaged in the field.
Amnesty International criticises assembly bans
For weeks students and students in France have been protesting, demanding better conditions and financing for schools. Protests have been joined by other street groups against high costs of living. Because of fear of riots and looting, such as those that occurred last weekend on the outskirts of demonstrations, authorities imposed assembly bans on specific areas of several cities and announced police hours.
The left populist candidate for president, Jean-Luc Mélenchon, who participated in the demonstration in Paris, said President Emmanuel Macron must understand that this will be repeated every week.
The Human Rights Organisation Amnesty International criticised the bans on gatherings and denounced what it described as a tendency towards authoritarian practices. /DW/