Some recent reading about the Crusades has made me realize that the Norman conquests of England (1066), Sicily (1130?), & the First Crusade (1096 onwards), all happened within a fairly short time period, but also well over a century after Rollo's treaty with Charles III (911 CE). My understanding of history is that a major expansionist drive for conquest doesn't really happen in a vacuum; there are conditions at home that lead to it (rising economic growth & military strength, domestic tensions that spill over, etc etc). I understood the First Crusade as being driven by Pope Urban II's drive to consolidate power, & fed by tensions in Europe, a knightly class, & a lot of second sons trying to escape a pretty awful situation in Europe. There were, of course, people from all over Western Europe in it, but as I understand it the leaders & Crusaders were disproportionately Norman & Frankish.
But thinking about the 1066-1096 timeline has me wanting more context. If it was simply their Viking heritage, why the long wait between settling in Normandy & then pushing outwards again? What was happening in the 11th century to drive the Normans to push out overseas?
The French (do not use "Frankish" to refer to people who lived centuries after the fall of the Frankish Empire and its dissolution into France and Germany in 843) had the biggest population in Europe, which is why they made for most of the Crusaders
As for the Normans, by the 11th century they were essentially French, but William's adventurous conquest of England gave them newfound political ambitions and a will to rival the French king (which they eventually did with the Angevin Empire).