First things first: the Duke of Alençon has nothing to do in this scenario. He only comes up in Joan’s saga much later, notably during the siege of Paris. The real historical character who supervised the military operations on the French side was the bastard of Orléans, Jean Dunois.
Oh, and by the way, Joan could ride a horse! She wore a red dress when she arrived in Vaucouleurs and was given men’s clothes to go on her journey at the request of Jean de Metz.