Rail workers and teachers staged one-day sympathy strikes on Tuesday across the country.
Early counts around the country suggested turnout could reach that of a week ago, when anything between one and three million took part.
France's ruling conservatives stopped short of agreeing to scrap the law but, faced with sliding poll ratings, signalled possible concessions to trade unions.
Dominique de Villepin, the prime minister, struck a defiant tone telling a rowdy parliament session the government would not "throw in the towel".
"The priority is to come out of the current crisis. It is not in the interest of anyone, especially not of the youth who are looking for jobs and awaiting solutions to their difficulties."
But Jacques Chirac, the president, has urged a softening of key parts of the legislation - for example halving the maximum duration of the trial period to a year - and his conservatives signalled further possible climb-downs on the measure.
"We'll be ready as of tomorrow to receive the unions, to listen to them. There won't be any limits to the talks," Bernard Accoyer, parliamentary chief of Chirac's Union for a Popular Movement (UMP) party, told French radio.
"I hope the demonstrations will help us deal it the fatal blow," said CGT union chief Bernard Thibault of the First Job Contract (CPE), which gives firms the right to summarily lay off workers under 26 during a two-year period.
Prime Minister Dominique de
Villepin is under pressure
Backers of the new law say it will free up the labour market by allowing employees to bypass French laws making it hard to lay off workers once on their books, whilst critics say it will discriminate against young people by making it easier to fire them.
Unions have vowed to resist overtures for talks unless ruling conservatives pledged to scrap the new laws and start anew on ways to tackle chronic youth joblessness which is stuck at 22%.
The mood on the Paris demonstration was festive and police were keeping a low-profile, mainly watching in side streets off the main route.
"The only solution is to scrap it (the law)," Lisa Mancin, an 18-year-old student said ahead of the main rally in central Paris.
More than a quarter of a million demonstrators earlier marched through the southern city of Marseille, organisers said, while up to 75,000 joined a rally in the western city of Nantes.
But disruption from the strikes was less than a week ago, and rail unions said 80% of trains were running across the country with city underground networks largely unaffected.
Air traffic was hit, with authorities estimating around a third of flights had been cancelled and others delayed.