By this period, the region had been firmly in Roman hands for a very long time. It's important to remember that 'nationality' is a very modern development for the most part, and during the Ancient period, your association was first and forrmost by tribe and/or regional polity, such as a city, not a national aspect. There were certainly some scattered ideas that arose momentarily that revolved around nationality, such as the attempt to unite the Germans in the first century AD, but they were always short lived. Rather than nationality, you might think of a 'culture'. In this case, the 'culture' would be Roman and/or Greek in most of the eastern Mediterranean. In the East, Greek was the dominant language of commerce and religion. That said, much of the region would have remained fundamentally Semitic in character (of which the Phoenicians and Jews were both branches of). Greek/Roman culture was centered around the 'Decapolis' and in these cities and their immediate environs we would expect Greek (and possibly Latin) to be the languages of the every day people. However, administration would still be in Greek/Latin throughout the region. So, while the common people in much of the Levant would have spoken a form of Semitic, the upper class in the cities would all almost certainly been fluent in Greek and likely Latin, and educated to Roman/Greek standards. Many would likely have considered themselves Roman. A good example of this is Procopius, a late historian of Antiquity/Early Medieval period who was from Caesarea, a Roman city on the Mediterranean coast.