I'm sure there's a name for this kind of fabric but I don't know what it is.
Sadly, this type of fur was very popular back then. Very young or even fetal Karakul lambs were prized for pelts. Newborn karakul sheep's pelts were called karakul (also spelled caracul), or astrakhan or krimmer in Russia. Newborn lambs have a tight, curly pattern of hair and must be under three days old when they are killed, or they will lose their black color and soft, tightly worn coils of fur. Dark colors are dominant and lambs often darken in color as they age. People used the lambs' pelts to create various clothing items, such as the karakul hat, or in haute couture.