Students and trade unions have called for another one-day strike next Tuesday in a drive to get the law scrapped.
If the Constitutional Council rules the law valid, it could be put into effect at once by President Jacques Chirac.
The president is expected to address the nation soon – possibly as early as Thursday evening, correspondents say.
Universities across the country have been disrupted for weeks by protests over the First Employment Contract (CPE), which would make it easier for employers to fire workers aged under 26.
Groups of up to 100 students continued small-scale demonstrations around the country on Thursday. Some occupied the tracks at Marseille and Rennes railway stations, stopping trains, while others blocked roads, causing traffic queues.