It would have to be an independent film, more than likely, due to the following problems it might have:
CAIR would go berserk and pressure the studios to not depict ANY misbehavior by Muslims at ALL during the fall of the city, in a similar manner to how they badgered Hollywood into changing the villains of "The Sum of All Fears" to some kind of elite cabal of Austrian Nazis (originally they were a coalition of radical Palestinians, a German Communist, and a Native American activist).
(It would be hilarious, in a really sad way, if thanks to CAIR complaints, they made the conquerors of the City Mongols or something with no Islamic references whatsoever, history be damned.)
However, at the same time, there'd be complaints from American cultural conservatives about portraying the Church, Christians, etc. a certain way.
Plus, do it "wrong" and the movie might be banned in certain countries, interfering with its marketability.
Perhaps we could persuade Mel Gibson that Constantinople fell because the Orthodox Church would not submit to reunion with Rome and he can fund it?
His "Passion of the Christ" was an indie film that made a colossal amount of money, after all.
And wouldn't this belong in Non-Political Chat?