I think maximum Persia would be Greece, Thrace, maybe Macedonia, and Carthage. I doubt the Achaemenids would be able to hold that land for a very long time. But if they were able to, I could see the regions being somewhat Persianized after a while.
Things would almost immediately get interesting (and unrecognizable) from then on out.
Much larger Persian cultural sphere?
Maybe the Romans are butterflied away...
Possibly a larger Greek immigration to Massalia (Marseilles), Hellenistic Gaul?