Like Rome did to the Greek. It won't be an overt conquest. European nations will still exsist, but there will be a supranational union over them (similar to the EU only with more power & defacto controlled by America).

Once democrats and RHINOs vote in healthcare, gun control/etc, there will be little resistance. Euros are already americanized beyond recognition and to apathetic/cynical to resist enmasse, and even if they do the immigrant vote will fuck them over (just like the 96 Quebec vote).

Besides euros/Canadians/etc having a direct vote/say in American politics is thier secret wet dream. All they need is serious crisis to get normies to willingly go along with it (world war china).