Napoleon’s temporary domination of Europe, at its peak between 1805 and 1812, was the very definition of an imbalance of power. But the other Answers fail to answer the question: How did the European “balance of power” change in regards to how powerful France and other powers were before Napoleon (and we should really say, before 1789 and the Revolutionary Period) in comparison to how the European balance of power, as formalized by the Congress of Vienna, ranked the powers after 1815 for many of the decades that followed?
France in 1789 was, despite dire budgetary problems and a clear slide in global influence in comparison to the U.K., still by far the strongest Continental European power in both the military and economic dimensions. This is precisely why it could overcome Revolutionary chaos and a coalition of all Europe against it between 1792 and 1795 and still prevail. On land, it overran Holland, the Rhineland and Northern Italy, and then kept all of its various opponents at bay, right up until Napoleon’s coup of the 18th Brumaire in 1799.
Napoleon then greatly strengthened the French State while gradually crushing the last hints of democracy within French institutions. After a spectacular run of military victories that saw almost all Europe subject to a new French Empire, Bonaparte’s overreach met its nemesis after his catastrophic invasion of Russia in 1812. With the defeats that followed in central Germany in 1813 and then in the bitterly resisted invasion of France itself during 1814, France found itself cut back to its boundaries of 1789. By 1815 its population was depleted, its navy all but destroyed and its overseas commerce all but wiped out.
Despite these blows, and the brief episode of the “100 Days,” the country actually recovered rather rapidly. By the 1820s, France’s commerce and industry were flourishing, and the slowdown in population growth that was to become a national obsession later in the 19th century was yet of little concern. The country had to tread cautiously in European politcs, but was almost fully rehabilitated.
The U.K. by 1815 was the world’s strongest power, vastly stronger than all its rivals. So much stronger that the only relevant modern comparison should be to the U.S. after 1945. As a result, the 19th Century could rather fairly be called “the British Century.” A truth illustrated by the rapidity with which Great Britain acquired control over more territory than any one power before or since ever has in the 1800s, comprising by 1900 nearly 25% of all the land on the planet! And the U.K. came also to exercise economic dominion over much of China (following the Opium Wars), not to neglect its political & economic control over India, first via the E.I.C and then later under direct rule; while becoming the dominant trade partner and investor in Latin America, most of the Middle East and beyond even earlier, in the immediate post-Napoleonic decades.
This said, it is a peculiar and significant fact that Britain, focused on global concerns, played a reluctant though nearly always key role in the European balance of power. While exerting tremendous influence, the U.K. stayed at a remove from most of the actual wars and crises of the 19th century, and actually stifled many potential conflicts by its strategic counter-balancing at the last opportune moment. The strongest power was typically the last to commit to a side; and often did so deliberately to even the odds and thereby deter war
Hope this helped, sorry if not.