I don't know about "enemies", but the EU was set up explicitly as an alternative market to the US. So, yes, they do want to compete with us and be better than us.
If the price of having "friends" is that we have a big difference in tariffs and trade balances, I think we could stand to have fewer friends.
Take note of the name of the alternative market: the social market economy. That’s imposed by treaty on all member states, but it originated in Adenauer’s West Germany. The only way it can be “better than us” is with the help of the left in the USA and their copying of the same method here to the detriment of the free market, thus depressing our competitiveness.
They also want to be a military power, so that is something that has to be prevented.