WI: France extends to the Rhine

During the partitions of the Carolingian Empire the West Frankish Kingdom does rather better than IOTL, and manages to get all Frankish territory west of the Rhine. How does this affect subsequent European history?
 
During the partitions of the Carolingian Empire the West Frankish Kingdom does rather better than IOTL, and manages to get all Frankish territory west of the Rhine. How does this affect subsequent European history?
You mean the West Francia annexes Middle Francia?
 
A basic pre-requisite, IMO, would be to screw Ottonian dynasty just enough to prevent them unifying enough the Kingdom of Germany and obtaining a large legitimacy and leadership trough their imperial project; and then enough power and influence (including within Western Francia) to held Carolingian claims in check.
Eventually, either trough a clear success of Arnulf of Bavaria over Conrad I (leading to a Luitpolding Germany), or Otto I dying before entering Italy (itself meaning Liutdolf becomes king, with a not that easy situation)

IOTL, a large part of Western Francian Carolingian legitimacy came from their ability to reclaim at least lower Lotharingia, and their unability to secure it was one of the reasons of their decline.
ITTL, you could see Late Carolingians remaining the leading dynasty over Robertians (that would likely enter in decline as IOTL) and beneficing as a political backbone from Lotharingia (not exactly a royal demense of sort, but stable enough to provide a political weight in face of western Francian magnates).

It could mean, that said, that the Western/Eastern Frankish - French/Teutonic conflicts doesn't fade away until the XIIth century as IOTL, but remain a main diplomatical feature with a shifting area (alliegance-wise) between Upper Lorraine and Burgundy. I'm not sure how much Carolingian WFrancia could hold of Lotharingia, due to a slightly lesser military power over the Xth century but if you weakened Ottonian or Luitpoldings enough, the Carolingian pressure might just be enough to secure at least a good chunk of it.

Carolingian France, no HRE, survivance of an at least technical imperial kingdom of Italy, main geopolitical focus over Rhine...All of this would have pretty much important consequence over the european development, so it's hard to really see where this is going : I'd say an overall greater Latin focus over Northern, Atlantic and Baltic Europe from one hand, and Burgundy while western and southern Europe becomes (even) more peripherical. But I don't think it would last much : it really goes down to who get tired to claim Lotharingia first.
 
For starters, the French Carolingians will need to perform better against the Norse raids. Also they need to have a secure military power base which means they will have to sooner or later deal with the Capetians who are in control of Paris and the Seine valley. Third the French Carolingians need to be able to fill archbishop / bishop vacancies concerning the French clergy without interference from the Holy Roman Emperor (Although the Holy Roman was in theory the de jure secular ruler of Western Christendom, Kings unlike dukes, counts, and barons were according to the medieval mindset the anointed representative of their kingdoms and thus needed to have a say over the appointment of archbishops / bishops in their realms). So basically you need to have a strong secure Carolingian monarch on the throne of France in order to have the French borders on the Rhine.
 
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