So, in OTL the Carolingian Empire was divided up in 843 along these lines creating East Francia, Middle Francia, and West Francia wherein all of Middle Francia would eventually become a part of the Holy Roman Empire which succeeded East Francia.
While they were all reunited very briefly, the division became permanent after 887. What if after this point West Francia were able to hold onto the Lotharingia portion of Middle Francia, within Burgundy/Provence and Italy falling into the HRE as per OTL, thereby preventing it from becoming a part of the Holy Roman Empire and becoming a part of France instead? Would Aachen/Aix-La-Chapelle remain the capital of West Francia/France?
While they were all reunited very briefly, the division became permanent after 887. What if after this point West Francia were able to hold onto the Lotharingia portion of Middle Francia, within Burgundy/Provence and Italy falling into the HRE as per OTL, thereby preventing it from becoming a part of the Holy Roman Empire and becoming a part of France instead? Would Aachen/Aix-La-Chapelle remain the capital of West Francia/France?