It's your fans. Specifically your CPU fan and GPU fan. Games always make your components work harder. If they didn't, the games would probably not be playable. The components generate more heat while working harder, so there needs to be more cooling going on. FF11 does not utilize graphics cards very well, so none of them really speed up from that game. It is normal in more or less every game, though.

New components will still work as hard as they can to give you the best possible performance in the game, though. New video cards might be just as loud as your old one, it depends on what sort of fans are being used. Small, radial fans are often more easily noticable than larger fans. You should probably go for a video card model that is advertised as "not as loud as the competitors" if you are sensitive to that sort of noise.