This refers to “new” vegetables, that is one from the start (or just before the start) of the season for the vegetable. They tend to be tastier and more tender than standard ones. Carottes primeur, for example, are said to be especially crunchy and juicy, with a fresh, sweet taste. They are available from April to July. Onions, leeks and potatoes are among other vegetables sold as primeur.
Primeur vegetables are often from warmer areas or grown under glass.
Pommes de terre primeur are subject to specific rules. They should be harvested before complete maturity and sold from January 1 to August 15 (at the start of this period they come from hot countries such as the French overseas territories). They are sold shortly after being harvested, unlike the ordinary “pommes de terre de conservation” - standard ones designed to be stored for long periods.
Primeur can also refer to a greengrocer specialising in such produce; while a vin primeur is one like Beaujolais Nouveau, sold shortly after it has been fermented.
Note the word primeur is invariable where it is associated with a vegetable type, though not where it refers to these early vegetables generally - les primeurs.