If we judge by Germany's handling of its own Gastarbeiter, the EU will handle it by burying its head in the sand and reviving the Voelkish definition that to be properly citizens of the individual EU states you have to be ethnic members of those states. Then the people who've lived there for several generations and are assimilated will wonder like Europe's Jews why the homeland of supposed tolerance keeps tripping over its own dick every time it has to actually implement that tolerance in practice (as opposed to America which has long made pious rhetoric and then done pogroms and lynchings shamelessly).