I expect that Americans and Europeans will be reasonably amiable. We will vacation and attend college in each other's countries, and (one hopes) trade as easily as Canada and the U.S. do today. But it will be China, India, Mexico, Indonesia, Brazil, Vietnam, the Arab world, and Turkey that the U.S. will have to huddle with most earnestly at important international conclaves--not Europe.
That is, frankly, not the circumstance most Americans would prefer. By rights, Europe and America ought to remain close cousins. But Europe's current choices in politics, economics, social and family life, and moral reasoning unmistakably suggest that a less familial relationship is emerging.
That is a reality that America needs to prepare for.