Roughly a third of the Russian Federation is in Europe, up to the Ural Mountains. The rest is, geographically, Asia. Around two thirds of the population lives in the European portion. The Russian Federation is also part of the Council of Europe.
Culturally, Russia has become progressively more European for several hundred years, but there are, and always have been Asian influences; many words used in bureaucracy derive from Mongolic languages, a number of well-known Russian writers names derive from Turkic, and at various times it was fashionable to assume a more or less Asian or European identity, amongst the nobility. Throughout the modern period of Russian writing, from Pushkin onwards, basically, there's been shifting emphasis from the Eastern, as in Lermonotovs "A Hero of Our Time", or Mayakovsky's "Scythians", to the Western, largely Francophone salon-culture of Pushkin or Blok's circles.
Especially amongst the Nouveau Riche, at the moment, there's a culture of conspicuous consumption of European fashion goods and so on, rather than buying domestic Russian brands, whch generally look exactly the same.