Would the Turks want that less than a "Greater Kurdistan" with half the population basically self-governed?
While Turkey's difficulties undoubtedly generate quite a bit of schadenfreude for some EU states like the France, the sticking point at this point is the fact that the Turks refuse to recognise the existence of another EU member state, Cyprus, and recognise another government in their place, a Turkish Cypriot government only recognized by Turkey. I have a difficult time imagining that the Turks can't understand why this is a legitimate problem.