At least 250,000 people took to the streets on Thursday in up to 80 towns and cities across France, according to police. Organisers put the figure as high as half a million.
Student leaders said 120,000 people marched through Paris's university quarter, although police said there were 30,000.
In Paris, a group of up to 300 masked protesters hurled missiles at police, who responded with tear gas and rubber pellets.
Eight officers were injured in the Paris violence and 10 were hurt elsewhere, police said.
Wave of protests
The planned First Employment Contract (CPE) allows employers to fire young people without reason in the first two years of their contracts in the hope this will encourage firms to be bolder in hiring.
Students say this discriminates against young people, and unions argue that firing employees without explanation is wrong in principle.
"You can't live with a knife at your throat," said 21-year-old film student Sophie Cojan, who joined the Paris protest.
Dominique de Villepin, the French prime minister, has championed the scheme as a key tool in fighting youth unemployment and is now facing the most serious test of his premiership as the wave of protests paralyses dozens of universities.
Strikes and sit-ins have spread to two-thirds of France's 84 universities, with 21 closed and 37 others badly disrupted, according to the education ministry, with protests also reported in dozens of schools.
Protesters say the law
discriminates against young people
Not all students back the protest movement, and clashes broke out in Toulouse as dozens of youths angry at the disruption to their studies tried to dislodge protesters from a building.
Villepin has said he is open to talks with union leaders but insists the measure - passed by parliament as part of a broader law on equal opportunities drawn up after November's riots - will be implemented.
Students at the Sorbonne university, a centre of the 1968 student protests that shook France, pelted police with stones and bottles and cracked the window of a bank before the police responded with tear gas.
Outside Paris, two officers and a student were slightly injured in scuffles pitting police against some 250 school students who were heading to the Paris march from the northern suburb of Raincy.
Six youths were arrested and two officers slightly injured after a rowdy protest by students forced the closure of a main road in Vitry-sur-Seine, southeast of Paris.
Large rallies were also held in Marseille, Lyon and Grenoble in the south and southeast, Bordeaux in the southwest, Rennes and Lille in the north, Clermont Ferrand, Limoges and Angers in the centre and Strasbourg in the east.
Violence erupted on the sidelines of the Rennes protest, where police fired tear gas at youths who set litter bins on fire and vandalised cars, some chanting: "Withdraw the CPE, or watch out!"