In some senses Russia, west of the Urals is close to Europe, and as far back as Peter the Great, the influence is there. French was the court language in Tolstoy’s time, but the Soviet Union was by its nature isolationist. So there’s an historical, cultural, and racial connection. But I’ve never heard it mentioned that Russia was ever a contender for EU membership. Trade ties and closer diplomatic ties, yes. Even countries the size of Poland and Turkey needed to be weighed up in light of their relative sizes. Russia would just be too big.
Russians do get a bit of a bad rap in Europe. I don’t think they are anymore arrogant that other peoples (I spent five months in Russia and speak Russian), but many gained new-found wealth very quickly and probably flashed it around a little too much for European tastes.
The EU was set up to counter US influence, and Eurasia is to counter both. I think that says it all about insecurities.
The game changer will be if Putin is tempted to send troops into eastern Ukraine. I believe he wants to, but the outcome may be too unpredictable. From what I can glean from the media, the pro-Russian troublemakers are few in number, so hopefully the situation will die down. The Ukrainian government is actually doing the right thing by not intervening. So perhaps they’re not all the belligerent thugs we first assumed.