Vintage shearling coat

Purchased this at the The Marché aux Puces de Saint-Ouen in Paris - flea market for 250$. I’m not sure if this is real shearling but the composition of the jacket is on the label and apparently lana means wool! Please note that this is a vintage jacket so there are a few scuffs and teeny holes - see pics. It’s a size xxl but added a pic of me wearing it for context. I’m 5’3 and 115 lbs- was looking for very oversized look. I selected size large on poshmark options as this is definitely not an xxl!