I'd imagine that the cultures would significantly mix but the Greek and Macedonians would likely have more influence than other cultures, language wise you'd probably get a system similar to the eastern roman empire, people speak their own language in their daily lives but anyone of importance will have to learn the language of their conquers to get the best education, trade opportunities and be able to remain of good terms with their Greek and Macedonian overlords. Additionally you have the large mostly Greek and Macedonian cities founded through out. These are likely to exert influence on the surrounding area due to be centres of commerce and learning.It's funny: another thread about Alexander living longer was posted just now. Seems that today is an Alexander-day. (Well, no complaints from me!)
Regarding this particular scenario, I feel obliged to point out what I did in the other thread, as well: the chances of Alexander living long enough to get an adult heir in place are slim. He had an unborn son by the time he died, and that's his heir. He won't start grooming some general or something: not unless his heir dies. So essentially you need a scenario wherein Alexander lives much longer-- preferably twinty years more, or something like that. Then he can leave his empire to his adult son, which is really the most stable thing to do. (Macedonian succession was notoriously messy: having a son as an undisputed heir is the best way to ensure things go smoothly.) Let's be honest: Alexander living twenty more years is, considering his extremely wild life, not exactly likely. It's frankly a miracle he lived as long as he did, considering how often he nearly died!
Yet I'll be the first to admit: the idea captivates me, too. Alexander living longer, founding a lasting empire? It certainly inspires me, and I happen to believe that if Alexander can live twenty more years (and if his heir is a capable administrator), the chances of this empire lasting for a good long time are actually fairly good (contrary to conventianal wisdom). Alexander himself was the weak point. He died before he was done; before he could cosolidate. But as I pointed out in the other thread just now:
My question, then, is simple: who exactly is going to be a threat of an empire that powerful? If Alexander lives twenty more years or so, that's plenty of time to carry through with his vision of culturally mixing his empire's populace. His army will be fully integrated, and loyal to the empire instead of to "Macedon", or "Greece", or "Persia".
I frankly admit that it has long been my wish to write a timeline on this exact topic. It may not be the most likely scenario, with the odds of Alexander living long enough being so low, but if we take that premise for granted, the resulting idea of a long-lived empire isn't so far-fetched. And very interesting...
On the subject of expansion I think if they did go as far as Marseille it wouldn't be for a vey long time but southern Italy and Sicily would be primary targets. North Africa would be harder to conquer and Carthage would most likely be able to offer a very good trading partner as they would desire goods from the east. As a result they might consider it more profitable to have them trade at good rates, pay tribute and five and maybe take over Carthaginian territories in Sicily. Going back to Marseille I think those territories might be a target for Rome and Carthage who could be prevented from expanding into Sicily and southern Italy.
While in his own life time Alexander may not have attempted to invade India but generations later leaders would be more familiar with India and would have the desire to do what Alexander couldn't to prove themselves and get their place in the history books.