Many schools and universities have been disrupted by the marches, with police in Paris put on alert. Protests became violent on Tuesday when police clashed with students holding a sit-in outside the capital's Sorbonne University.
More demonstrations are planned for Saturday and trades unions are urging up to a million people to take to the streets.
Between 7,000 and 15,000 students marched in the city of Marseilles, according to police sources and protest organisers respectively and large demonstrations have also taken place in Grenoble, Limoges and Le Havre, with thousands more protesters marching in a dozen other towns.
Students fear the First Employment Contract (CPE), passed into law last week, will take away job security in a country where more than 20% of 18- to 25-year-olds are unemployed.
