Alexander was ancient Macedonian, not Greek. He was multi lingual though. In Alex's time, Macedon used Greek in their official stuff, and Alexander received a Greek education. The Greek philosopher Aristotle taught Alexander. Alex chose Greek as the official language of his empire.
No one really knows what other language the ancient Macedonians spoke, since we don't have manuscripts using it. Alexander's people later resisted Roman rule. The Romans were not pleased. The people sojourning there today are different people, and use a different language.