The scenario proposed by Eurofed is effectively ineresting, although I'm not totally satisifed with it...
First, there is Napoleon. I think he knew what was to come to him in 1815 when he did his last campaign and Waterloo : he had all of Europe against him and would have to defeat all the allied armies one by one before they could join force, something he failed to do OTL. However, here we have a different situation... The Allies are divided between Britain and Austria on one side and Russia and Prussia on the other side.
Napoleon is no fool : I think he can understand that having the Allies fighting each other will be his best option to rebuild France's power and to keep the throne would be to let the Allies fight one another and quietly rebuild the Grand Army. That's not such a bad plan and Napoleon has all the qualities to succeed : he is a brilliant general, popular (There wouldn't have been the Hundred Days if l'Empereur had not been) and is far from stupid.
Napoleon could also choose to help one side, which brings out why I'm not really satisfied with Eurofed's scenario : The British's role. Britain's policy was and as always been to keep balance between European powers.
What thread does Napoleon pose by the time of the Congress of Vienna? True, the Emperor is a great general and proved it more than once. But France was defeated in the Napoleonic Wars and greatly suffered. So, he probably is not in a strong position and is (in my opinion) a threat that is less important than the Russio-Prussians.
I'm probably proposing an heresy, but it could be possible for Britain to choose to let Napoleon recover his throne in exchange for his alliance against Prussia and Russia...
Napoleon can also choose to go for the Russio-Prussians, but I doubt he will do it. First, Alexander doesn't like Napoleon and second he is seen as a monster in Prussia (he destroyed there army in only ONE battle : Iena-Auesterdt). I'm not sure if he can go for a "no alliance" or "three way war" tactics as none of these scenario are in his favor.
Lastly, there is Murat's role. If I'm not wrong, the Austrians were the ones to bribe Murat into betraying Napoleon... So why would he go to the Russian's side? It would seem more likely for him to ally the Austrians.
I don't really know how likely my scenario is... But here would be the outline :
-War happens because the Russians call the bluff in the Polish-Saxon crisis. The allies divide themselves between Britain-Austria on one side and Russia-Prussia on the other side.
-Murat goes for the Austro-British in hopes of keeping his kingdom of Naples because of what was promised to him when he betrayed Napoleon.
-Napoleon returns from Elba. He recovers power in France and force the French Bourbons into Exile. He then strenghten his position in France and propose an alliance to Britain and Austria.
-The British accept Napoleon's offer as they know the Russo-Prussians are in a stronger position than the Austro-British. A deal is made in which Napoleon keeps his throne (and maybe France's natural borders) in exchange for declaring war on the Russo-Prussians.
After that, it depends on how the war goes on...
1°) The Russo-Prussian wins. The situation would turn similar to Eurofed's scenario, maybe with a Bourbon restoration in France and Naples (due to Murat and Napoleon fighting on the British side)
2°) The Austro-British and Napoleon wins, which would be the scenario I would go for due to personnal preferences. In this scenario, Napoleon could win a seat in Vienna (ironically) and keep his throne, maybe with France's natural borders. Murat would also keep his throne, Saxony would be still on the Map and Poland might stay independant as a punishment to both Prussia and Russia.
This scenario would also see some sort of cold war between Western Europe (lead by Britain, Napoleonic France and Austria) and Eastern Europe (lead by Russia and Prussia). It would also had some glory to Napoleon as, despite being defeated in 1814, he rises frome his ashes like a Phoenix. Don't know how likely this is, but it is awesome
In any case, the Polish-Saxon crisis is probably an interesting POD for a Napoleonic timeline...