Most of Normandy, including the capital Rouen, 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 successively whittled down in importance and size over the following centuries. By the time the Normans arrived, 'Neustria' would have been a loose geographic term referring to the lands between the Seine and the Loire. So Neustria didn't exist in any real administrative sense and certainly wasn't a proto-Normandy.

And, of course, these were exceptionally fluid frontiers with Bretons, Flemings and others occupying various chunks of modern Normandy. The closest there would have been to a central authority in the area was the archdiocese of Rouen.