score:2
As your wife, she enjoys freedom of movement under EU law whenever she travels with you or to join you. This right is not dependent on her having any documentation beyond a valid passport. You should bring a copy of your marriage certificate to prove your relationship if you are challenged by any police or other government authorities.
The airline may have additional documentation requirements, which you should check, but since you have not said which airline it is, we can't help you with that.