The Byzantine Empire was a new phase of the Roman (Empire), as the Principate, Republic, Kingdom and Dominate had been before. It had a good run, until either failing in 1204 or moving on to basically a Palaiologos Kingdom (of 'Rome').
France is (at minimum) continuous since Philippe Auguste, but the French Republic was vastly different than the Kingdom of France Philippe had created, and Vichy France was a nice limbo until De Gaulle resurrected France, but it's all still France. Sure, it shares the capital (well Vichy not so much), so it has a bit more continuity than Byzantium has straight from Augustus or Romulus, but there's also layers inbetween that make Byzantium the same state.
Nothing stops you from discussing just Byzantium, though, or just the classical Romans, if you want to. It's somewhat fuzzy where it transits, exactly, and it's possible to group them together, but noone's gonna be surprised if you call Basil II a Byzantine or Augustus a Roman.
So, in other words, the question is still stupid even if I think the answer isn't actually no.
France is (at minimum) continuous since Philippe Auguste, but the French Republic was vastly different than the Kingdom of France Philippe had created, and Vichy France was a nice limbo until De Gaulle resurrected France, but it's all still France. Sure, it shares the capital (well Vichy not so much), so it has a bit more continuity than Byzantium has straight from Augustus or Romulus, but there's also layers inbetween that make Byzantium the same state.
Nothing stops you from discussing just Byzantium, though, or just the classical Romans, if you want to. It's somewhat fuzzy where it transits, exactly, and it's possible to group them together, but noone's gonna be surprised if you call Basil II a Byzantine or Augustus a Roman.
So, in other words, the question is still stupid even if I think the answer isn't actually no.