According to The Flow of History, during the French Revolution, European monarchs feared that France's revolutionary ideas would spread, leading to rebellion in their own kingdoms. Napoleon affected Europe dramatically, causing changes that would take dire political work to change. Even after his defeat, the countries of Europe went to great lengths to stabilize.
France was the inspiration for outbreaks of revolution all over Europe, spreading all of the way to South America, between 1815 and 1848. Napoleon spread liberalism through Western and Central Europe, nationalism through Central Europe and to the East. Monarchs across the affected countries maintained a thin veil of peace through this time, only to see it disturbed by these rebellious outbursts periodically.
The French Revolution was met with an odd sort of defeated success, as the allied monarchs of the rest of Europe struggled to restore the balance of power in their favor. Through nearly debilitating deliberations, they decided that the only way to do this was to restore France to its old position. Otherwise, they knew they would be risking the frail balance of power and the stability of all of Europe, and nearly guaranteeing continued revolutions that could possibly be worse than that of France. Napoleon knew that his ideas would spread, and despite his defeat, they did.