Yes, that would be the key change necessary. By a mix of succession law changes and sons dying off, the biggest, OTL proto-national subdivisions of the empire ruled by the cadet members of the Imperial line stay feudal-ish Viceroyalty subunits of an undivided WRE, subordinate to the eldest son as the one Emperor, not de facto, soon de jure independent kingdoms, till the end of the 9th century, and the precedent gets entrenched. From that on, it becomes the usual centralization task of the Western monarchies. If Capetian France could do it, so can the Carolingian WRE that spawned it.
I suppose there's a few more factors that need to be overcome. I'd suggest you can "Byzantinise" the state (build it a bureaucracy and a tradition of centralisation) by having the "Western Emperor" marrying a couple of Byzantine princesses, like the Ottonians did. Maybe having stronger Magyars could act as some sort of incentive to "unify or die" for the proto-Western state, or maybe have the Arabs break out more strongly into France? A more traumatic than OTL fifty years around 900, with Arabs, Vikings, and Magyars pushing in from all sides could do a lot to help the state, in the long run.
The Papacy obviously needs to be thoroughly dominated, too, with the Church structures co-opted into the state as much, or maybe even further, than they were in the East.