It's going to be hard : Charles I Crownkemon (Gotta Catch'em All!) had neither the ressources or the political possibility to undergo such conquest and to maintain it.
Between wars in Italy, unsuccessful campaigns in Hellada or Epirus, being so overly ambitious he made the Pope and the Byzantine emperor allying against him, and the deep disinterest of French Capetians (his main support) into wasting ressource into desilusional campaigns or (and that say a lot from Louis IX) desilusional Crusades...
That said, I could see Charles being more successful in Balkans, such as managing to hold for him both Epirus and establishing his domination over remaining Latin States in the regions (with a bonus, maybe central Hellada) as Latin Emperor.
But going for Constantinople, would it be only giving that his flanks were far too open to reverse alliances (even if only de facto ones) or inner troubles? Even if he would manage to do that, the lack of manpower and troubles in Italy would force him to eventually give up IMO.
Don't get me wrong : it would have been a drain for Palaloigos, and would have significantly weakened Byzantium, making its decline even more quick, maybe with another Byzantine successors splitting up.
But the big winners would have been Serbians and Bulgarians rather than Angevines.