Issuing their ultimatum on Saturday, the leaders said they might decide on a one-day general strike unless the government withdrew the law by Monday evening.
The leaders said Jacques Chirac, the French president, and Dominique de Villepin, the prime minister, would "bear full responsibility for social tensions that might follow" if they failed to meet the deadline.
The marches were mostly festive and peaceful, but dozens of youths pelted police with missiles, set a car ablaze and smashed a shop window at the end of the main protest in Paris. Police cleared them from the Place de la Nation with many rounds of teargas.
Scattered violence was also reported in Marseille, Rennes and Lille, where police also charged and teargassed crowds.
Rene Valadon, confederal secretary of the Force Ouvriere union, after union and student leaders met following the third nationwide protest in six weeks, said: "This is an ultimatum, the government and the president have 48 hours to decide."
Organisers estimated the turnout nationwide at 1.3 to 1.4 million, with up to 400,000 of them in Paris. The official count was lower - the Interior Ministry reported 503,000 nationwide, with 80,000 in Paris.
In the government's first reaction, spokesman Jean-Francois Cope said: "Beyond the passions of the moment, don't we all have an interest in a dialogue?" He ducked a television interviewer's question whether the government would withdraw the law.
"I risk working for two years for nothing"
Coralie Huvet, a student
Villepin launched the new employment contract to spur wary employers to take on new staff, but critics decry it as a "Kleenex contract" that lets young workers be "thrown away like a paper tissue".
Coralie Huvet, a 20-year-old student marching in Paris, said: "I risk working for two years for nothing, just to be fired at any moment."
She had "No to the CPE" written on her forehead, a reference to the first job contract (CPE) the protesters oppose because it lets firms fire workers under 26 without explanation during their first two years on the job.
In the western city of Rennes, a stronghold of the three national protests in the past six weeks, students marched in plastic rubbish bags with signs declaring: "I am disposable."
The demonstrators were a multi-generational mix of students and older workers, including many parents who accompanied their teenage children. Banners declared "No to throw-away youths" and "Tired Of Being Squeezed Lemons."
Opposition socialist and communist politicians also joined the protest, only the third time in almost four decades - after 1968 and 1994 - that students and workers marched together.
In the Paris unrest, 12 protesters were injured and 59 detained, police said, while four policemen were also hurt.
In Rennes, police had to storm a group of protesters to remove them from a railway line they were blocking. Another group attacked an office of Chirac's governing UMP party.
Villepin, whose gamble on this unpopular contract could cost him his chance to run for president next year, has pledged not to give in to street pressure. At the same time, he hinted on Friday evening that he could make some adjustments to the law.
Unemployment is the top political issue in France, where the national average is 9.6% and youth joblessness is double that. The rate rises to 40-50% in some of the poor suburbs hit by several weeks of youth rioting last autumn.
Clashes broke out between
protesters and police
Latest opinion polls show that 68% of French people oppose the law, a rise of 13 percentage points in a week, and that Villepin's popularity has dropped six points to 37%.
The crisis has isolated Villepin politically at a time when his mentor Chirac is himself badly weakened. The interior minister, Nicolas Sarkozy - Villepin's main rival on the right - has stood back discreetly as the prime minister's troubles mount.