It's unclear if "Europe" wants anything of the sort at this point, and you seem to assume that English would be the common language, which is not unreasonable since it's the one currently being used, but it's not politically acceptable, and it'll be worse if the UK finally decides to leave.

Note also that Europe is probably the part of the world where minority languages are in better shape. E.g Catalan is spoken by 4 million native speakers, which is more than all of the native american language speakers combined.