First thing first: Constantine actually lived until 879, outliving Louis of Italy. His planned marriage with Ermengarda is shrouded in the mists of time, though, most likely being called off after the events of 871; as the conquest of Bari broke the opportunistic alliance between the prospective in-laws over by then usual rivalry between Frankish and Byzantine imperial pretenses and the natural clash of interests over South Italy. So, you need a POD that makes either Bari go worse - maybe prompting a Byzantine landing by Constantine himself - or just take long enough; the marriage happens and Ermengarda is "safely" imprisoned in a gilded cage at Constantinople.
There still are a lot of problems in store, though, for this Crusader Kings-style scheme to go anywhere.
As mentioned in passing, chauvinism would get in the way of the best scenario; Constantine is not going to go away from his father's side, live at the court of the Frankish pretender, or set up a dangerously distant (and exposed) court in Italy that Louis would certainly come to see as a threat. So this most likely prevents Constantine from really being ready to seize the chance when it presents, and being seen by the non-Greek populace as one of them. The Lombard polities of the south are still fiercely independent, and haven't certainly ever liked Byzantium; the Arab raiders are a threat in waiting, and kept taking Byzantine fortresses in eastern Sicily, so they need to be neutralized before any move northwards is ever attempted; and last but not least, relations with Rome were still strained over the recent Photian schism and the influence tug of war over the newly-Christianised Bulgarians and Slavs on top of the old grievances.
All these things combined make it likely that Constantine's rights are ignored, with OTL pretenders like Carloman of Bavaria and Charles the Bald coming in and successfully seizing all lands north of Capua in accord with the Pope and the Italian populace who, unlike the 6th Century, no longer identifies as much (if at all) with the Empire in the East.
As said, I believe that only swift and successful intervention from a Constantine that happens to be there, capable and ready to strike, have any chance of succeeding beyond the Greek-speaking lands of the South (and even then, it needs a lot of sixes; OTL the Byzantines merely managed to seize most of Apulia and Calabria in the chaos following the disintegration of Karling power in Italy).
