Since the medieval Roman Emperor title went with protecting the Pope, any medieval Roman Empire will include Italy. I dunno. Sadly, Germanys fracturing IOTL was no direct result of Roman Empire status. German Kings will likely still be elected, seeing as how Germany after the Carolingians was basically a confederaion of tribal duchies. And the direction of France in that regard would be purely up to butterflies too, I think.
There were serious attempts to centralize the German Kingdom and make it an hereditary monarchy under the Ottonians and the Hohenstaufens. It is reasonable to assume that without the stress and the distraction of the interventions in Italy, some of them would have been successful. OTOH, now it is the King of France that has to deal with the same problems in dealing with the Popes and the Italian communes. If the Imperial title goes to France, I can totally see the fates of Germany and France being completely reversed, which makes Germany a strong successful centralized nation-state and France the Balkanized playground of the English, the Germans, and the Spanish for the next few centuries. I wonder which of the French big feudal states would get to play the role of the Habsburg, if any.
A strong Middle Age Germany leads to the complete assimilation of the Czech and I can see the Drang Nach Osten going further than ITOL, with most of Poland and Hungary being Germanized.
I wonder which part united Germany would play in the colonization of the Americas. I guess it very much depends whether the Low Countries end up a part of Germany, or of France, the latter a contested area between Germany and England.
Does the PoD alter the boundaries of the Carolingian partition at the treaty of Verdun ?