It would have interesting implications for Italy and Germany, at least in the short to medium term. With that kind of prestige (and obvious divine favour) on Otto's part, I can't see Frederick gaining much traction as the 'legitimate' emperor. At the same time, neither he nor the pope are liable to back off, so we're likely to see a Holy Roman Emperor in control of much of the Empire in direct contravention of papal decree and winning. With the money Otto is liable to take away from the venture and his considerable Hausmacht, he'll be hard to depose. I can't see much of an effect on France (maybe Flanders seizes the opportunity to remove itself more, and King John might make some temporary gains). Emperor Otto will be too focused on Italy, and the economic and political power of France proper remains untouched. Even an exorbitant ransom did not ruin England, and I don't think his lords will allow Otto to demand that much for a captive French king.
So, Italy. The worst possible idea (and perhaps the most likely one
) would be Investiture Contest 2.0. Otto comes roaring down the mountains and
a) takes Rome, instals his own pope, and leaves, finding this has zero effect in the long run
b) suffers a nasty defeat at the hands of Lombard militias and looks like an idiot
c) manages to capture/kill/drive away Frederick and conquer Sicily as well as deposing the pope?
I don't think any of these things will have a lasting effect on the HRE, though all would likely hurt Otto in the medium term. What would be ever so cool would be a two-state solution with Frederick playing Emperor in Sicily and Otto reigning in Germany. On the one hand, it would create a Mediterranean imperial state with real potential down the line (the resources of Sicily and the power of the papal-aligned maritime republics would be in line, at least initially, and the Med is a target-rich environment: Malta, the Balearics, Anbdalusia various North African statelets, maybe a dynastic union with Barcelona...) On the other, it would give the emperor a real stake in developing political power in Germany at a crucial juncture and make the papacy look terminally weak. There may be a German-induced Anagni in its immediate future.
This could get interesting.