Or one might ask this:
• What exactly makes a European state European?
- Why is Turkey a European country but Algeria is not?
- Why is Iceland a European country but Morocco is not?
The factors of Europeanness are mainly genetic, cultural and historical. Some also add a linguistic factor.
Based on these factors, Iceland, Norway, Belarus, Ukraine, Russia are completely eligible. Turkey, Armenia, Georgia and Kazakhstan would be eligible as long as history is concerned. Linguistically Armenia is Indo-European, but so is most of South Asia. Historically and genetically modern Europeans can trace their roots to Anatolia, the Caucasus and the Pontic-Caspian steppe. It's ironic that none of these regions are even candidate for EU membership.
Whether Europe's geography ends before or after the Caucasus and the Urals is a matter of definition. But it is 100% clear that North Africa is not Europe.
Genetically North Africa has less in common with Europe than Central Asia, Iran, Afghanistan or Pakistan.
What makes Turkey eligible? Is it only the small part of the West Bosporus that could just as well have remained Greek? If Morocco conquers Gibraltar from Britain, can they then join?
Turkey's connection with Europe runs much deeper than the Greek heritage. During the Neolithic Europe was recolonised by farmers and herders from Syria and southern Anatolia. During the Bronze-Age the Indo-European expansion could have started from all the Black Sea shores, including northern Anatolia. The oldest branches of IE languages are the Anatolian ones, so there is a chance that European languages (except Finn, Estonian, Hungarian and Basque) originated in northern Turkey.
If you look at the genetics of modern Turkish people, 75% of the paternal lineages are the same as in Europe (the rest is 15% Arabic and 10% East/Central Asian). Kazakhstan has two distinct population : a Mongolian-descended majority and a European Russian minority. Tajikistan would be more eligible genetically.
I think these are important questions, and not as easy to answer that it might seem. The answer explains why Europe's border ends in Caucasus and not in the Middle-East or China. With answers to those questions, could you please explain exactly why French Guyana or the Canary Islands could not be sovereign states in the EU, and why culture and ethnicity should not have precedence? It seems the French views Reunion and French Guyana as as much as part of France as Provence or Normandie. There has to be a rationale behind the EU membership as well. Is it only by proxy the Falkland Islands is a part of EU? Can we say to people "Yes, you are Europeans but the land you live on is not traditionally considered so, hence you cannot become a member."?
France, like the United States, tends to take a non-ethnic view of citizenship. But that's the mainstream of politicians who think so, not necessarily the people.
I know it's not the same, but Hawaii is not a part of America per se, but still became an American state, and it might just be that Guam could reach statehood.
The USA was not built on geography. The EU is a post-colonial system aimed at reinforcing Europe after two world wars and the loss of its colonies. If you want to include non-European countries like Canada, Australia or Argentina into the EU as overseas states of a greater state, that you nearly amount to neo-colonialism. Anyway, do these countries really want to join the EU ?
Unless there is an overwhelming consensus towards joining the EU in at least one of them, and Europeans see it favourably, there is no ground for a debate about it.
It's hard to imagine Quebec or Uruguay sending members of parliament to Brussels. It's easy in itself, but they would be so far away from the member-state they represent. There are Brits who already complain that Brussels is too far (2 hours by Eurostar from London !) and feel they are ruled by a foreign power !