European affairs had a huge impact on the United States during this time. Most significantly, European affairs almost got the United States into a war with France and then actually did help to cause a war between the US and Great Britain (this was the War of 1812).
During this time period, the most important European event was the rise of Napoleon and the wars that his rise set off. The central players in these wars were Britain and France. The US got caught up in these wars because both sides wanted to prevent the US from trading with the other side. This led both sides to violate the US's right to free navigation. The taking of US ships on the high seas led to the near-war with France and the War of 1812.