The Italian War interests me as it has one of my favourite historical figures in it- Savaranola. Savaranola's mastership of Florence rested on his brilliant rhetoric and also because the Florentine Republic had, under the Medicis, reached its apex and was then declining. He saw Charles as the wrath of God brought upon Italy and so when Charles began losing in Itay Savaranola lost favour and was eventually outflanked by the Pope.
If Charles won, say he manages to get through to the Papal States, Florence gives him aid and he knocks Alexander VI out of the war before taking Naples with his massive artillery train, then I'd imagine these things would happen.
1. He'd probably either annex Lombardy (not likely) or put a cadet branch of the French royal family in Milan (quite likely) or just make a nobody Duke (less likely but more savvy-they'd be easier to control which is necessary with the Alps between them).
2. Charles would make himself King of Naples, which makes sense, yet he probably couldn't take Sicily, at least not at that time or in that campaign. Holding Naples would allow France to exercise far more power overthe Papal Elections, so there would be less corruption on th ebehalf of the Italian church that used the post to enrich themselves. Not saying there'd be any huge reform, but there would be at least a wideing of the church's upper echelons. This could, perhaps, have an effect upon the reformation although probably not a huge amount. It would probably mean less French Protestantism.
3. Savaranola would probably last a bit longer, ta least into the 16th century, and indeed he could last even longer. Even if he managed to remain the leader of Florence until his death (his natural death that is) his regime would probably fracture after his death. It relied on his charisma and rhetoric and so without him it would probably fall over pretty quickly (think the English Commonwealth for an easy parallel). I think, however, that the Florentine Republic would last longer as it wouldn't have powerful enemies in Milan or Rome. France is more detached and so would be less concerned with Florentine power. Machiavelli would make things interesting.
There may be some furor in the Holy Roman Empire over Charles's meddling in Italy (parts of which were in the HRE and Rome has always had a tricky relationship with the Empire) although I couldn't imagine the outcome. Maybe war but given the HRE hadn't been too concerned with hte Pope since the 13th century I'd doubt it.
There may be large effects in Venice, perhaps without Milan to counterbalance it it takes more Italian territory, maybe it is decisively defeated by France, I don't know.