I don't really know enough European history. It's long, it's complicated, and in the end, it often comes down to a some guys who really hated each other getting large numbers of people killed.
I admit that's something of an oversimplification.
In any case, much of what follows comes from some conversations I've had with Dave Stout, a fellow who knows his history far better than I do. However, all errors that follow are mine, because that's the way this goes.
The American Revolution was a wondrous thing from European eyes, reflecting (or at least seeming to) the ideology of The Enlightenment, with all the rights of man, scientific principles, etc. that were so much in fashion. There was also the "Nostalgie de la Boue" thing that Tom Wolfe has written about, literally, "Nostalgia for the Mud" but more figuratively, the "romanticizing of primitive souls." I remember a tale from high school history (and hence very suspect) that Ben Franklin's first appearance before the court of France came before he'd had a chance to unpack, so he could not wear his powdered wig. His naked head charmed the French aristos, him being a child of the wilderness and all. And so clever.
So old Ben became a Rock Star in his seventies, in Paris, and took to just a charming anyone who'd come around, including, it was rumored (and kinda said outright by John Adams) practically anyone in a skirt. I find it difficult to be shocked. Or, for that matter, surprised.
There was apparently something of an "egalitarian" fad before the French Revolution, with all sorts of aristocrats and privileged folk deciding that it would be a good idea to get to know their servants and others among the "little people." I'm bound to wonder if that helped or hurt their chances when the great guillotine lottery came to town. I can see it going either way. It's a "laws and sausages" thing from either side.
The French Revolution scared everybody in Europe, and by "everybody" I mean all the powerful folks whose necks began to itch at odd intervals. France itself was a mess; one of the features of the American Revolution was that, if things got too feisty in one area or another, a bunch of folk would just pull up stakes and move on. In France, there wasn't really any "on" to move to. It also turns out that all those principles of The Enlightenment, can squish around as much as Biblical text in producing whatever result one has in mind. Who knew?
Anyway, France had been at war with various other European powers for quite a while prior to the Revolution; the King's military spending was, in fact, one of the commonly cited factors for the country's near bankruptcy, which in turn gave the Revolution a good headlong shove. Add to that the fact that there was this grand social experiment going on (one which was explicitly rejecting the "divine right of Kings," and, for that matter, "the diving right of the Pope"), and the surrounding countries were not neutral observers.
So there followed a series of "Coalitions" amongst the Great Nations of Europe, sending armies to bite off as much of France as the situation would allow, and if the Revolution could be forced into collapse, so much the better.
The problem was, and here I specifically note Dave's excellent imagery, the "Coalitions" generally amounted to coming at France more or less the same way that ninja come at Bruce Lee in a Kung Fu movie, i.e. without much in the way of coordination. Britain could more or less kick anybody's ass at sea, but the land campaigns from Italy, Prussia, Austria, et al. were of the "our guys will just go in and brush them aside" (I'm unable to find a direct Dr. Strangelove link) sorts of deals. So they kept losing.
And as they were losing, the best commanders and tacticians in the French military (now cleared of a lot of deadwood by the aforementioned guillotine) were rising to the occasion. And rising in rank.
Napoleon is the obvious result, but there were a number of other pretty smart guys who gave a pretty good show, like Carnot, Jourdan, Moreau, and the like. Napoleon just happened to be the cream of the cream, and his nationality (Corsica being Italian, well, okay, Genoan, until it's purchase by France in 1768) made it easy for him to snap up Italy early on.
He eventually overreached, as so many do, and that story is pretty well known, what with the Russian winter, massive loss of men, and exile to palindromic Elba. Then there was the "over the hill boxer coming out of retirement" deal, and "The Hundred Days" ending in Waterloo, blah, blah, blah. There was also a thing called "The Holy Alliance" (catchy name; it got reused), that tried to put Humpty Dumpty back together again, and managed to do pretty well, provided you ignored the fact that a number of the new kings and other royals weren't quite exactly who they would have been before Napoleon.
So we get the 19th Century, with the nations of Europe playing Risk with the rest of the world, all the while all the Royals looked over their shoulders, wary of the next mob, the next Commune, the next guillotine, or the next Napoleon. Actually, they didn't mind the next Napoleon so much, since he put scotch to the second French Republic. Besides it was those damned Republics that they really hated, and all those weird democratic notions that The Enlightenment had put out there.
The next grand "popular fashion" was a romanticization of war, an epidemic of war fever, and what was called at the time, The Great War.
Some didn't think it so great, but you've got to break some eggs to make some Dada.
In The Great War, aka WWI, we had the famous sealed train sending Lenin into Russia to make as much trouble as possible (they had a low estimate on what "as possible" meant). The Brits carved up the Ottoman Empire into what they considered manageable bites, and they missed that by a margin as well. The U.S. backed a lot of petty dictators because they were "bulwarks against communism" and for those efforts we got a theocratic Iran, after the Shah fell, theocratic Afghanistan (because, really, what kind of harm could a bunch or armed fanatical Muslims do to us?), and (in case I've been too subtle) a nuclear Pakistan teetering on the brink of collapse because it turns out that when you invade or otherwise meddle in other countries, there can be unexpected consequences.
Well, who would have expected that?