Senators pass reforms by 195 votes to 112, bringing the package another step towards becoming law.
Police fired tear gas to push back black-clad protesters who ransacked business premises during May Day demonstrations against the policies of President Emmanuel Macron.
Inspired by Canadian truckers paralysing border traffic with the United States, the demonstrators include anti-Covid vaccination activists and people angry at fast-rising energy prices.
Interior Minister Gerard Darmanin says police arrested 95 people while 67 officers were injured during violent street clashes over a controversial security bill.
Demonstrators gather for the 16th straight weekend in Paris and other cities to protest President Emmanuel Macron's economic policies which they say favours country's rich.
Three opposition parties, the Socialist Party, far-left Defiant France and the Communist Party are setting aside their divisions and promise to submit a request to seek a no-confidence vote in the lower house of parliament.
President Emmanuel Macron is also set to address the country later in the day as he seeks to placate "yellow vest" anti-government protesters who wreaked havoc in Paris this weekend.
The announcement from the main agricultural union comes as France's President Emmanuel Macron approved a six-month suspension of fuel tax a day earlier in a move to end violent "yellow vest" protests.
The French Human Rights League organised Sunday's protest in Paris following the alleged rape of a suspect by a police officer last month.
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