What existed at this time was the "March of Neustria", that was a non-unifided command against Viking and Breton raids.
Part of it was controlled or under Robertian influence (Robertians being the direct ancestors of Capetians), the other (the "norman" part) was under Berengar's rule whom ascendency is hard to establish, maybe a branch of Popponids (or part of main one) that was more or less related to Robertians.
Without Rollo becoming Count of Rouen, Robertians/Capetians would have a better deal on western Francia but would have still to deal with continued raids from Brittany and Norses.
While Robertian/Capetian takeover of Western Francia seems pretty much unavoidable at this time, and I can see Robert being crowned as OTL, maybe in position to put the Robertian/Capetian dynasty in place in the early X Century rather than in the latter part.
It could mean earlier stabilisation of WF, with the possible re-conquest or holding of Lotharingia for them that went close OTL.
On the other hand, Ramnulfids consolidated their power in the same time. Guilhèm I isn't going to be that much enthusiast about a Robertian takeover : they'll likely use the same tactic than IOTL, aka taking a carolingian pretender as rally banner.
Depending on how well they do, you could avoid, limit or seriously increase the "sucession war" of Aquitaine in the middle of X century.
No such war and earlier stabilisation of Western Francia and Aquitaine could have an important social consequence : the "Paix de Dieu" movement, led by church, managed to manage feudal anarchy (but not feudal lords themselves) and critically to increase the clerical role on society giving it a clear independence from laics lords.
It could lead to interesting changes for gregorian reforms, and how church manages to put his influence on medieval world, maybe (if well turned) no Crusade. Butit's not a direct consequence of No Normandy, rather how No Normandy would lead to stronger Robertians in early X, then possible confrontation with Ramnuflids and Carolingians that could prevent or increase civil disorder. What I say is of course valid only in the first case.
Returning to the point :
I don't think Bretons would have the ressources to take western Neustria. Nerfed Robertians are going to be a serious obstacle. While attacked by raids, Robertians and Carolingians, Normans managed to kick Bretons easily. I don't see why Super-Robert would have an harder time.
No Normandy wouldn't mean no Norse presence in Neustria : there were already there (even if coastal, shores and more outpost than actual settlements) and could replace (without being equivalent) the scandinavian settlement IOTL.
Culturally, it would mean less words coming from Scandinavian in french, but outside that...
Considering Normans were almost fully integrated on the Gallo-Frankish population by the XI century, I don't think someone would really notice a difference.