This depends on what years are included in the "late 20th century" in your mind.
If we are talking about the time late in and especially after the Cold War, the US had little impact on European political structures but a great deal of impact on its culture. Earlier in the century, the US had more of an impact on the political development as well.
During the early Cold War period, the US had a major impact on European politics. It created the Marshall Plan to help European countries' economies and to ensure that the Europeans remained democratic. It helped to create the state of West Germany. It helped provide security for all of Western Europe.
As the Cold War ended, so did this impact. The American culture then came to have more of an impact. Perhaps the most visible sign of this cultural impact came with the opening of Disneyland Paris in 1992.