Strangely enough I am reading an Osprey book about Medieval Scandinavain Armies 1300 to 1500. I just finished 1100 to 1300.

He needs:
A helmet.
A bigger shield, maybe with a guige, and maybe it should be a different shape as well.
A bigger axe or a sword.
The sleeves on the hauberk could be longer to protect his lower arms.
Mail mittens to protect his hands.
Some slits along the sides of the botton of the hauberk, so he can move better.

Other than that it is fine.