"Je veux qu'elle ferme ce livre."
Because word by word translated it is "I want that she closes that book" and then you use the 3ps form.
Someone who knows more can correct me if I'm wrong, but I believe that after a conjunction, in this case "que", the next verb has to be conjugated as normal. You also see this in the "I live to eat and eat to live." sentence that sometimes gets asked.