The Revolutionary and Napoleonic Wars were resolved by the Seventh Coalition in 1815, establishing a delicate balance of power known as the Concert of Europe. This ushered in an unprecedented era of peace for the continent, which would not see another major pan European conflict for almost a century until the outbreak of WW1 in 1914. Despite its successes, the Concert was inherently unstable, and its ultimate failure can in many ways be attributed to the legacies of the French revolution. The Concert depended on maintaining the balance of power as it was in 1815, but the forces unleashed by the French revolution grew over the nineteenth century, despite attempts to suppress them, undermining the Concert and eventually causing its total collapse in WW1. These forces can essentially be boiled down into two types: economic and political.
The British borrowed heavily to finance their war with France. The Emancipation of the Jews enabled the Rothschild family to rise to prominence in this activity, pioneering as they did so much of modern financial capitalism, a development which would later help stimulate the industrial revolution. This revolution spread unevenly over Europe. At the end of the Napoleonic Wars Prussia was granted land in the German Rhineland, territory it was soon discovered, that contained vast deposits of coal and which would greatly support Prussia’s rise and unification of Germany. France meanwhile did not industrialise at the same pace and its population remained fairly stable while its neighbours grew rapidly. This is partly due to the legacy of the French revolution. Land redistribution discouraged large families, and the damaging effects of the war would hamper growth for years to come.
One of the most significant political legacies of the French revolution was the rise of nationalism. In the words of Paul Raynaud, before the national unifications of the nineteenth century, France was a ‘giant among pygmies’ in Europe, after it neither France nor any part of the Concert had the power (or in many cases the inclination) to maintain the prevailing order. In 1806, Napoleon abolished the ancient Holy Roman Empire. This would have two major consequences as far as WW1 is concerned, it would lead to the formation of the Prussian dominated German Empire in 1871, and the Austrian Empire’s turning away from Central Europe, looking instead to the lands of the Ottoman Empire for expansion. This would culminate in 1914 with the assassination of Archduke Franz Ferdinand by Serbian nationalists and the outbreak of the war. In addition Russia’s entry into the war on the side of Serbia was influenced by its own nationalist, pan-slavist, movement.
On a more direct level without the French Revolution there could never have been Napoleon III. Brought to prominence by his famous ancestry and in many ways locked in its shadow, Napoleon III did much to undermine the delicate balance of the Concert. His alliance with Piedmont-Sardinia enabled the unification of Italy, and his disastrous war with Prussia the unification of Germany. Also, the loss in that war of the industrialised Alsace and Lorraine provinces to Germany would be a source of simmering national resentment between the two countries until WW1.
EDIT: PS The French wars, and the attempted blockade of Britain, would encourage that country to deepen its ties with its imperial colonies. This would contribute to the 19th century British policy of 'splendid isolation' from Europe. What was in many ways the continent's greatest power at that time did its best to ignore the political upheavals there, leaving a vacuum at the heart of the European Concert.