It may not be my place to speak as I have never played a single Final Fantasy Game in my life but thanks to the multiple fanfictions and the wikia, I am of the opinion that the only two FF series that could possibly work with a TYPE-MOON Crossover are VII & X.
One is a world on the verge of ending due to corporate assholes and nutcases, not to mention said corporation is nearly completely corrupt. VII sounds like a place where a quite a few individuals [Shirou included] would fit in fairly well, especially if Shirou's merry band of companions [Rin, Archer, Sakura, Rider, Illya, Saber, & Taiga] and maybe a few other servants arrived in Wutai before Shinra invaded, they could both fight and defend the people of Wutai.
The Second world, where technology is shunned and a creature known as SIN runs rampant. Again another world where characters and servants could blend in while fighting the main threats to said world.
Anyways I have a Crossover idea of my own to present
Fate Stay/Night x Cardcaptor Sakura
The main issues with this crossover is how Zouken would deal with the Clow Cards, no doubt he'd try and use them to his gain but as Sakura is to be their mistress, he can't make Sakura make Shinji the new master of the cards due to him having no magic ability of his own.