Well, didn't the Frankokratia managed to "go native" and adopt Orthodox Christianity after the expulsion of the Venetians? After all, that managed to endear them to the population a bit and thus solidify their reign.
Yeah the Sicilian excommunication and the creation of The Most Serene Republic of Italy supported by the papacy really backfired them, this resulted in the schism of the West and the popularity of the Crusaders really increased after that and in the end the pro-Avignon league finally adopted the Orthodox Christianity which greatly reduced tensions with local in the Frankokratians state.
But they never really became native, I mean they adopted a lot of local custom, some words, ... But the French is still the administrative language in these areas and
the language of the elite (even the common language in some states), they played each minorities against the others and we see the French and Sicilian influence everywhere, you know Frankokratians state still encourage the French-speaking immigration.
It's more a merger these states often consider themselves as French-Greek, French-Armenian, French-Syriac, ...
But yes without this conversion the crusaders would still be considered as oppressor and would never acquire the religious support. The Greeks would eventually revolt en masse and some will try to took profit of this.
Moreover the war against the papacy (we fought together against a common enemy) and the expulsion of Venetians (the Greek, French, Sicilians, ... the scapegoat of a lot of their problems) allow them to unite.
Thanks now i get a lot of POD

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But in your opinion
What would this world like ?
I mean a lot of butterfly would happened, this world would be so different