The Napoleonic Wars in Europe had a great deal to do with the War of 1812.
First, the British were understandably much more concerned with the wars in Europe than they were with fighting the United States. This meant that they did not devote their full power to fighting the US. Of course, this made it much easier for the US to avoid defeat.
Second, the British victory in Europe in 1814 made them more willing to come to an agreement with the US. They had won their major fight and were busy trying to reshape the map of Europe at the Congress of Vienna.
In these ways, the Napoleonic Wars did a great deal to help the United States avoid defeat in the War of 1812 and get a settlement after the war that would be satisfactory to them.