Unions and student groups were celebrating victory after President Jacques Chirac bowed to two months of strikes and street protests by dropping the plan.
But protesters said they would remain "vigilant" until a substitute law was voted in.
Debate was due to start late on Tuesday in the National Assembly on the measures to replace the First Employment Contract (CPE), and a vote was due within days.
Following the climbdown -- seen as a personal failure for Prime Minister Dominique de Villepin -- thousands of students descended into the streets, with many calling for more concessions on employment.
"Scrapping the CPE was a minimum," said Romain, 22, a student in southwestern Toulouse, where police said about 2,500 people marched in the city centre. "The unions were in a position to ask for more."
But the protests remained small-scale -- with 600 demonstrators in southern Marseille and 1,000 in Paris, eastern Grenoble and Rennes in the northwest -- compared to the million-strong rallies of recent weeks.
Students also blocked bus depots in Toulouse, briefly invaded runways at Nantes airport in the west and occupied a radio station in Grenoble.
Four French universities remained closed down by strikes, with 27 others disrupted, despite a call by a national student leader for classes to resume.
Some students have now set their sights on a repeal of the entire law that brought in the CPE.
The law on equal opportunities, drawn up following November's suburban riots, also includes a controversial provision lowering the minimum age for apprenticeships to 14.
They also want the repeal of the CPE's sister contract, the New Employment Contract (CNE), introduced last year for employees of small companies.
Mr Villepin's CPE, a contract for under-26 year-olds that could be broken off without reason during a two-year trial period, is now to be replaced by new state subsidies to encourage companies to take on unqualified young staff.
In a sign of appeasement, however, unions said they were prepared to join a national debate on labour flexibility -- a notion reviled by many in France -- following a call by business groups.
Addressing the National Assembly, Mr Villepin told deputies that "the only question that counts, is what we are doing to fight youth unemployment".
"We want to learn from this crisis," he said. "We want to answer French people's social concerns, their worries about the future."
Within the centre-right, the CPE debacle has brought about a power shift that is expected to weigh on next year's presidential election.