The fitted jacket that European men commonly wore during the Renaissance period is called a doublet. If you go to a Renaissance Faire, you'll see men wearing doublets (along with cloaks, tunics, tights, and scabbards).
The French word doublet comes from duble, "double or two-fold." The original doublets were merely the lining (or "doubling") of another garment, often a hauberk, or chainmail shirt, and meant to keep the stiff material from rubbing or chafing the skin. The doublet evolved into being worn on its own, tailored to fit the body and sometimes padded to give the wearer a "fashionable" shape.