Sorry but they would speak greek...Just like Royal English court would use french as language during a short period of time...It does not mean they did not also speak english.
But upper classes Roman knew also latin of course.For example,when stabbed Julius Caesar never said to Brutus "tu quoque mi fili" but rather "Kai su teknon".
Voila!
\Thank you for an interesting reply to my rather rude response; a Google search supports your view. I knew that the Byzantine Empire shifted to or maintained Greek and ( from Gibbon's
Decline and Fall) that Greek nurses would instruct their charges in Latin and Greek, but did not know that it was as widely used among the high born as, say, french was in the Russian court before the fall of the Empire..
Your reference to Caesar's dying words also has great speculative entertainment value. The most famous "furrin" quotation from Shakespeare changes "my son" to Brutus's name, "Et tu, Brute?" Which to a Roman bystander might have meant, "You too, stupid?" I suspect that the traditional belief that Shakespeare's Julius spoke in Latin is true, but as a schoolchild, when translating Latin Prepared I was required to translate Greek passages into French, so it is possible that Shakespeare, who had "small Latin and less Greek" was offering a poorly remembered French translation from an English rendering of a Latin text. Of course, a Francophone would probably hear "Et tu Brute" as "And you, raw?" but the English have always had a proud tradition of being bad at languages, and King George V, trying to call down the blessing of God on French troops around 1914, thought that "blesser" was the verb to bless! [and for those of us who have forgotten much of their french, "blesser" mean "to injure", so the French troops were a little disturbed to hear this foreign monarch say "May God wound you"]
Anyway, I am happy to concede the point and thank you for getting my tired old brain working for half an hour or so.