This is the Chasseur Alpin's field uniform winter version of the Tarte (in 200 grams weight!); a beret that is, even in France, very hard to find. These black Tartes Alpin in 320mm diameter (sizes up to 59) and 330mm diameter (sizes over 59) are not fitted with a headband, but have a thick wool rim which is sized, making these berets extremely comfortable and well fitting. It also allows for some choice if you prefer a tight fitting beret, you can safely choose one or two sizes down or the other way around if you prefer a more relaxed fit.
The Béret Alpin was designed for, and is used for, sentry duties in the sub zero conditions of the high Alps; for downhill skiing without the beret flying off the head and is typically used to warm the feet while wet boots dry on bivouac.
