Gîte à la noix in French butchery refers to a specific cut of beef known as the "round" or "topside" in English, specifically a part of the round near the rump of the cow. The term gîte à la noix translates roughly to "lodging to the nut," which is a somewhat playful way of referring to the round, bulbous shape of this cut of meat.
The gîte à la noix is a lean cut that's best when slow-cooked, as in a roast, or when sliced thinly against the grain. It's often used in dishes that require long, slow cooking to break down the fibers in the meat and make it tender, like pot roasts and stews.