The French would take a "business as usual attitude" as a "betrayal" he warned.
The presidential candidate attempted to explain the benefits of globalisation to workers at a Whirlpool factory who are losing their jobs due to the factory relocating to Poland.
The National Front traditionally holds a May Day march in Paris to honour Joan of Arc.
There were five arrests in all.
Fears that a high abstention rate could help far-right candidate Marine Le Pen in France's presidential runoff strengthened Tuesday when two-thirds of far-left supporters said they intend to abstain or cast a blank ballot.
"Not one or the other; instead it's the people's self-defence" read one sign.
However aides of Ms Le Pen attempted to brush off the criticism.
The moderate CFDT union marked the May Day holiday with a small Paris rally against Le Pen, leader of the National Front party. Le Pen launched a full-throttled attack on her opponent, painting presidential candidate Emmanuel Macron as a clone of the unpopular current President Francois Hollande.
Protesters battle through tear gas grenades during Paris clashes.
Pour parler de la France, Marine Le Pen est obligée de plagier MOT POUR MOT un discours de Fillon ...
US trade deficit narrows in March
The data agency further reported that energy products and consumer goods were responsible for much of the increase in exports. Exports dropped 0.9 percent to $191 billion, pulled down by falling auto exports.
Ms Le Pen also evoked a quote from early 20th century French Prime Minister Georges Clemenceau which had him stating:"Once a soldier of God, and now a soldier of Liberty, France will always be the soldier of the ideal".
Macron, a former economy minister, is campaigning on strong pro-European, pro-free market, liberal views. Then-party leader Jean-Marie Le Pen sought to distance himself from the attackers, but the death drew national outrage.
Philharmonic director Laurent Bayle said: "We who want to keep living in societies based on differences, we need step up the effort through this week and call a maximum of people to spread our message of friendship".
Macron's economic liberalism worries many voters on the left.
Protesters push a burning trolley towards police during violent scenes in central Paris at May Day march. So I will vote for him.
French Presidential frontrunner Emmanuel Macron speaks at a campaign rally in Paris on May 1. Macron "was the only member of the "system" who opposed" the harsh stance on Greece, Varoufakis said. "That is why I am fighting, to say "No" to racism".
The far-right hopeful added that her party and Fillon's voters share "the same vision of France, of its greatness, of the role it should have in the world".
Marine Le Pen tweeted her support for the injured policemen and said the incident was the type of unacceptable behaviour that she no longer wanted to see on French streets.
Polls consider Mr Macron the front-runner in the run-off but the race has been unpredictable. "One of them is a candidate who will uphold republican values and one is not".