Found a great chiropracter at last and these really are the best shoes for an arch that tends to fall inwards meaning you walk on the inner side of your heel as we do, watch the inner ankles and see if they are held more straight by this shoe, it means your back is better in line and you are less likely to end up with a slightly hunched neck look like me, wish I had known this years ago!!!
They are wide. However I have narrow feet and wear the narrow and wide Birkis and find the wide ones slightly more comfy. Somehow your foot sits comfortably in the middle so I expect my daughters narrow feet with be fine too with this width. Before you send them back for being too wide watch your child walk in them and see if the foot stays in position.
The sizing info says a 12 is a size 30, however when you add a 12 to your basket it comes up a size 31, which is a size 13. I didn't notice the European size on the order as I am not familiar with them and they were way too big.