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At least 5000 officers were on duty in Paris alone on Sunday, with water cannons and armoured cars also deployed on the streets of the French capital.
Tear gas and baton charges were used against a mob close to Place de la Bastille, as banks and a McDonalds fast food outlet were attacked.
“The violence appears organised and directed at specific targets,” said an eye witness.
“Guys with black hoods and balaclavas are smashing stuff up while others scream for Macron to resign.”
It followed street violence breaking out a week ago, when Mr Macron won a second term by beating far-Right rival Marine Le Pen in the presidential election.
“The May Day mobilisation must be as massive as possible,” said Philippe Martinez, general secretary of the General Confederation of Labour – France’s largest trade union.
“Beyond the unions, citizens must take to the streets so as to make sure their social and environmental demands are made loud and clear.”
Marches and meetings were being held across France, including in major cities beyond Paris, such as Marseille, Nantes and Toulouse.
Radical groups due to take part included the Yellow Vests, who were behind regular riots in major cities such as Paris throughout Mr Macron’s first term.
Anarchists who frequently target buildings including banks and upmarket shops were also due to infiltrate the crowds.
“Some 5000 police and gendarmes are on duty, and they include riot control units,”said a Paris police source.
“May Day usually attracts crowds of up to 20,000, and this year is not expected to be any different.”
There is particular anger at the spiralling cost of living, and Mr Macron’s plans to raise the pension age from 62 to 65.
Others – including the Yellow Vests – are unhappy with the entire system of government in France, saying that too much power is invested in the president.
Jean-Luc Melenchon, the hard-Left politician who came third in this year’s presidential election, was one of those leading the May Day march in Paris on Sunday.
It was between two of the great protest squares in the city – Republic and Nation.
Melenchon has called for all Left Wing parties to “unite, and to regain the will to win”, in time for legislative elections in June.
Mr Melenchon’s aim is to deprive Mr Macron of a working majority in the National Assembly, so making it harder for him to govern.
May Day was in 1889 chosen as the date for International Workers’ Day by the Socialists and Communists of the Second International.