I can’t say I know how much of the EU will be left, or what it will look like, during the Trump Administration. That will depend to some extent on the outcome of December’s Italian referendum, and more on the French election next year.
Assuming, for purposes of argument, that the EU soldiers on pretty much as before, its relations with the US are likely to be pretty frosty, because Trump will perceive it as a weak talking shop that preaches too much about human rights, does little to control terrorists, and runs a huge trade surplus with the US. My guess is that Turkey will be the first flash point (Trump will support Erdogan’s crackdown, but the EU won’t), and things will just deteriorate from there.
The ultimate beneficiary of this, of course, will be Putin.