Europe has no common "basis language." It is a linguistic mosaic with 24 official EU languages and 60+ regional/minority languages.
Indo-European (Germanic, Romance, Slavic, Celtic, Baltic, Hellenic, Albanian, Armenian), Uralic (Finnish, Hungarian, Sami), Turkic (Tatar, Bashkir, Gagauz), Semitic (Maltese), isolates (Basque).
English is the de facto bridge language, but no language is "the basis" of Europe. Multilingualism is the norm; the EU operates on "unity in diversity."