Though there nevers was a "Norman Empire" as such, the normans did have quite an impact on medieval Europe, conquering England and Sicily amongst other places and profoundly changing those countries. They were also important players in many other European wars like the early crusades.
But what if there never were any Normans? What if Rollo the walker somehow had been stopped from becoming ruler of Normandy (and no other viking chief did also) and that region simply remained a part of northern France?