"Masked individuals threw objects and Molotov cocktails at police" who responded by firing teargas, authorities said.
The violence erupted near Place de la Bastille in the French capital as the march led by three unions including France's biggest, the CGT, headed for another square nearby.
At one point, a blazing shopping trolley packed with flammable material was pushed towards police lines, an AFP photographer saw.
The rivals for the presidency, centrist frontrunner Emmanuel Macron and far-right rival Marine Le Pen, faced shows of opposition to their programmes during the fractious May 1 workers' marches.