"The stronger the mobilisation for this May Day, the harder we will be able to weigh on the government's policies," Philippe Martinez, the head of the hardline CGT union, told Reuters before the rallies.
"The government has got to deal with the purchasing power problem by raising wages," he said.
Macron won a new five-year presidential term after beating far-right challenger Marine Le Pen in last Sunday's runoff vote.
Far-left leader Jean-Luc Melenchon, who came third in the first round of the presidential vote, was attending the Paris march.
He wants to rally a union of the left, including the Greens, to dominate parliament and force Macron into an awkward "cohabitation" but so far this has not materialised.
"We will not make a single concession on pensions," Melenchon said before the march started.
He said he still hoped an agreement to build a new "popular union" of the left could be reached by this evening.
Unlike in previous years, Marine Le Pen did not lay a wreath in Paris at the statue of Joan or Arc, whom her party uses as a nationalist symbol. She was replaced by the Rassemblement National Interim President Jordan Bardella, who said Le Pen was preparing for the legislative elections.
Le Pen urged voters in a video message to elect as many deputies from her party as possible in June so that she could "protect your purchasing power," and prevent Macron from carrying a "harmful project for France and the French people"
France will hold parliamentary elections on June 12 and 19.
