Critics of the law, which makes it easy for employers to make young employees redundant, say it damages the protection traditionally given to workers but the government argues the law is necessary to combat high youth unemployment figures.
However, the government has asked French employers not to apply it until amendments are made.
On Friday, President Jacques Chirac pledged to shorten from two years to one the period in which young people could be fired, and he also said that employers would need to give a reason for dismissal.
The trade unions say the proposed amendments are unacceptable and at Tuesday's protests, there were some scuffles between protestors and police in Paris.
A spokesman for trade union CGT said that 3.1 million people had turned out nationwide, but police say it was just over one million.
