Exactly. It looks like OP is referring is the nation-state in the European sense, which is an invention of the late 19th century only. In this understanding, nation=group with same language, ethnicity, "values", and state is indeed the political entity in which said nation (=group) lives.
So it means that all of this isn't even 2 centuries old, but it has indeed shaped the minds to such an extent that we think it's the only way to go. But if you take any Euro nation-state, they all have very different "nations" in them. France for example has Basques, Bretons, Occitans etc...you don't hear about them now because they were culturally crushed by the central government in Paris, precisely to establish the "nation-state". The mistake you make, no offense, is that you use the US frame of "race" so you see all French people are white, so they're the same "nation". Nope, it's a construct. And that's not even talking about Euro countries with real separatist movements, such as Belgium, Spain, Italy. And obviously, the fact that the nation-state and the new-foound patriotism (and its ugly-cousin nationalism) is one of the main reasons for WW1.
So even on the continent that invented the concept of nation-state (Europe), that concept is shaky at best and is under serious discussion at all levels. If you go back in history all the major empires were an insane mix of various ethnicities, languages, etc. It's the so-called "rationalism" that led people to believe that simplifying things (one nation one language one ethnicity) would be better. Problem is, people move, languages travel, cultures change. So instead of finding ways of living together (as in olden days), you're looking for ways to move towards that elusive "unicity", which means putting up borders (hence the invention of ID and passports in that same area) and finding ways to define who's in and who's out. With all the xenopoby and racism that ensues.
Actually if you look around the world very few countries are "nation" unified. None on continental Western, Central, Eastern Europe or the Balkans, that's for sure. Not even GB. MAYBE Norway and them, Greenland, Iceland. I doubt any Asian country is (even Japan has aborigenal type populations in the north that have damn near been eradicated), African countries def not, Middle-East neither, America (the continent) obviously not.
So this idea of a nation-state in the sense of a homogeneous group (or race) = a country hardly exists anywhere.