This is a very good question, and one weird thing about pre 1500 history is how you these high energy groups of people that arise from the middle of nowhere and create havoc, then after a few centuries nothing is heard of them. It could be the much smaller population sizes (the world had less than 500 million people total before 1500) that does this, which increases the standard deviation of groups from the norm and also means that small groups of people by our standards could have huge impacts.
IOTL, the Normans had three areas of operation:
1. England and northern France being the most famous area. One interesting thing about this is that the William the Conqueror did not have any grandsons in the male line that survived past 1135, so both England and Normandy wound up being fought over by the French houses of Anjou and Blois. This suggests that there may have been nothing special about Normandy, some other Continental based dynasty, maybe from Flanders if not Anjour or Blois, would have taken over England.
2. Southern Italy, which might be a bigger deal than England because the Normans effectively created a new kingdom and took on and beat everyone else in the neighborhood (the Byzantines, the Germans, the Papacy, and the Sicilian Arabs) seemingly without much difficulty. Without the Normans, the Salians might have moved in like the Hohenstaufen did later, but its not clear what happens. Its also not clear if Muslim Sicily survives or was on its way out anyway, same with the Byzantines who were declining anyway would would have had an easier time without the Normans.
3. The Crusades/ the Levant, since the Normans did give a boost to the First Crusade and the Crusader states in general.
There is a possibility of England being less entangled with the Continent and more in the Scandinavia orbit, but just removing the Normans far from guarantees it. I really have no idea what happens in the Sicilian power vacuum.