Aside from the obvious things with her being a woman, lower class, and claiming to hear angels talking to her.
It seems odd to me that somebody with no education or experience in military matters was able to pick up an army and win victories when the French had been struggling in general.
Joan of Arc was a tremendous asset to French morale, but she was by no means the principle strategist of the French war effort. The infamous Gilles de Rais (baron, favorite of the Duke of Brittany, Marshall of the Crown and serial child killer), one of Joan's companions, was in many respects a more conventional war leader whose influence on the strategic dimensions of the conflict is often overlooked in favor of the more poetic image of Joan as an inspiring commander.
I asked a similar question once and got some interesting responses: