This is going to be series of questions based on the answers of the previous ones if thats all right.
Question No.1: So why was France included in the Congress of Vienna, being a defeated power and all.
I hate to come off as annoying, and maybe our local Francophile /u/DonaldFDraper would be more willing to play 20 questions, but I find it much easier to answer a series of questions if I know where the questions are leading and can tackle it in one big post so I can build everything off of each other and know how to approach certain topics rather than making a bunch of 250-500 word posts in complete vacuums without context.
Your curiosity clearly isn't centered around why France wasn't included in the Congress but some questions built off of that as you say yourself. Or maybe it is. That's the issue, I don't know what you really want here but just the first part to a long series of interrogation questions that hopefully by the end would give me some idea of what you really want. By doing it this way I don't know what's important and what's not to getting the point across and may focus on entirely the wrong things for expressing a certain point you may be building up around asking about.
So really, what are the things you are wanting to know and we can tackle them a bit more cohesively knowing where your questioning is going rather than answering a series of vague questions? Even if you don't want to just post a list of questions at least giving a general idea of where your reasoning is trying to go with this mysterious line of questioning would be helpful.
I am not a historian, I am only a young guy who is interested in history, but I'll try to answer this:
The Congress of Vienna took place to restore the political conditions of 1792. So France was the bad guy (from the view of all the others) during the war, but it wasn't lead by a king of the House of Bourbon, instead Napoleon was the leader and emperor.
The Congress of Vienna gave France back to it's 'rightful' owner, the House of Bourbon. It was different from negotiations after the Second World War where Nazi-Germany and its allies clearly where the villains from the view of the winners, while after Napoleon's defeat they gave France back to the true king.
It all would be leading up to if the Congress of Vienna accomplished its goal of having the Great Powers balance each other out. I would think otherwise considering there was a fair amount of war (and a world war almost 100 years later)