If sitting with legs crossed was different enough to become known as sitting Indian Style how did Europeans sit when they didn't have a chair?

"Tailor's fashion" is the older term for the same sitting style. Tailors sit cross-legged upon the board (table) rather than at it on a chair. It's a term still used in some European nations today and dates back very far. It's done this way to tighten up the back muscles so they don't wear out as quickly. In fact, studies have been done on tailors bodies that showed quite a few changes due to the constant sitting in this manner. The blood vessels enlarged to keep the legs from falling asleep and the long muscle that reaches from the pelvis into the tibia is longer than in normal people, hence why it is now termed the Sartorius muscle (word for tailor).

edited to correct the medical info that ExpectedChaos provided