How 'European' does your country feel?
I assume you mean how much of a EU citizen we feel?
I am Portuguese and Portugal is very pro-EU. That does not mean that we follow every single thing. For example we were very affected by the austerity measures and there were soon anti-austerity retorics started. And until now have been pretty successful Portugal shows there is an alternative to austerity | Letters
This is the beauty of the EU. You can even have UKIP in the EU. More democratic than that you can't have. And the EU admits when it was wrong. The EU has prized Portugal and admited that was not expecting this economic change with the measures that were taken (Investment instead of more austerity).
I have always prized EU for being the most successful peace project of our time. And for defending EU citizens rigths. And our environment.
And since Brexit we have had several demostrations of that. Since it made sure that the 3 key points included citizens rigths, Ireland and North Ireland boarder and the bill.
While everyone likes to point that countries that have big trading relations with the UK will step in (Germany, France and Netherlands) the truth is that until now the EU always have put Ireland as having the final word.
And EU has offered from the start a way better deal to British citizens in the EU, and tried to get one for EU citizens in the UK (before any trade talks). In fact even offered an opt-in to UK citizens in EU. And at this moment British citizens have a case with ECJ and may even keep their EU citizenship independently of the brexit negotiations.
So yes pretty happy about EU.
I have seen the EU being the escape goat for politicians in several countries and the punching bag of many newspapers but some of the things are easily found as BS. I am not saying EU is perfect, but the EU is open for improvement.
I think that the answer depends totally on your expectations on what Europeanness should feel like.
Europe is big enough to stretch from the African borders to the Arctic regions and deep into the Russian taiga at the Ural mountains. I can't imagine one Europeanness within that area.
Even if the question possible mixes Europe with the EU, the area still covers so many cultural areas that it's hard to imagine what Europeanness should feel like from Malta to Alta.
My country, Finland, feels totally European, but it certainly doesn't feel the same as Greece or Italy.
If the question wants to ask how strongly we feel a part of the EU, the answer is that the EU has quite a strong support in Finland. We are not the most pro-EU country, but definitely supporting our membership despite the visible opposing groups..
If by European you mean "European", then I'd say that Serbia feels quite European given that we are in Europe and are connected to the continent through many different things.
If European in this case refers to the European Union, then I don't think that it affects our view on being European, but I'd guess that there is probably a feeling of disconnection.