That's not how it works. They'd be protected by a formation of men with shields and then jump in when the enemy looks exposed. The two-handed axes could smash apart enemy shields, which would turn the tide of a push.
Also, they most likely wore shields on their backs and swords or axes at their waist. The dane axe (two handed axe) was too slow to hold up in a melee. They'd do a few strikes with it and drop it when it was time to get out of dodge. But it was a very useful utility weapon.
I suppose if the man was lucky, he would have turned around and hoped the arrows impacted his shield. Because this is a fictional artwork, sheer luck keeps him protected against arrows while the shield is simply dangling on his back.
Also, if he were a true-to-life huscarl, he probably would have crouched down where the archers couldn't see him until it was time to strike. The power of fictional representation makes this guy influence fate through being 'hardcore' though.