It's not the same thing. Your analogies show an inaccurate view of the situation. The French, from Hugh Capet to Emanuel Macron show a lot more continuity and national continuum in many ways than the Byzantine Empire has to the Roman Empire, which is really just, all in all, political pretense. And, recognizing political pretense alone as a continuation of national continuum is a VERY controversial path to follow, let me tell you. For instance, it would also mean that the Holy Roman Empire, the Austrian Empire, the Russian Empire, Napoleon's French Empire, the Ottoman Empire, itself, the early Medieval Serbian and Bulgarian Empires, the modern Greek irredentist, "Megali Idea," and Mussolini's Fascist Kingdom of Italy, as well as the Roman Catholic Church on a, "sacredoutum mundi," must be seen as continuations of the Roman Empire, because they all hold a political pretense of some sort or another. Hell, even the United States founding fathers invoking ideals, symbols, terminology, and District of Columbia mall architecture from the Roman Republic is very evocative. Thus, saying a civ had a pretense of Roman continuity as being, "Roman," and not worthy of a separate civ slot quickly ludicrous to sustain.