To expand on an old post, most of what became Normandy was part of the larger Frankish province called Neustria. Originally one of the key Merovingian kingdoms, stretching from today's Belgium/German border to the Bay of Biscay, it was whittled down in importance and size over the following centuries. By the time the Normans arrived 'Neustria' would have been little more than a loose geographic term referring to the lands between the Seine and the Loire.

So, with the exception of some marcher lords, Neustria didn't exist in any real administrative sense and certainly wasn't a proto-Normandy. The closest there would have been to a central authority in the area was the archdiocese of Rouen, which covered most of the later province. But Bretons, Flemings and others all occupied various chunks of modern Normandy and it took decades for the eventual borders of the province to take shape.