Actually, the Normans are treated by the papacy as Foederati in Italy against the Byzantines.
Thing is, the Normans were the sons and grandsons of the men defeated by Alfred. In this TL these alt sons. are based in Wessex and perhaps include a grandchild or two of 'Alfred the Unready' among them, or at least the men that followed him.Truth be told, it did. The Normans were just Vikings who had spent a bit of time in Western France getting bulked up.
However, had Guthrum managed to defeat Alfred comprehensively (and likely fatally on the battlefield) the ongoing wars for control of the Danish Kingdom might not have resulted in loss of England back to the Anglo-Saxons. Question then really becomes if, at some point, the Normans decide to have a go at their cousins. If they don't you can easily wind up with a Scandinavian Empire that stretches from Kiev to the Davis Strait, maybe even Far Eastern Labrador.
Normans were not Norse. Most of Rollo's warriors already took French wives and the next generation was bo more Norse than an average Frenchman