In 1480 the Ottomans took a port in southern Italy, in preparation for a campaign to take Italy. Mehmed II, the Sultan who conquered Constantinople, was at the head of an invading army when he suddenly died at the young age of 49. Lets say that he doesn't die for 10 years. He leads an invasion of Italy, bringing the West's Monarchies into Italian politics 15 years ahead of OTL. The Spanish were preparing to invade Granada, but with the Ottoman threat to Rome, I'm going to bet they want to protect the Holy See. The Spanish may end up being the only monarchy who has a long-term interest in fighting in Italy. The French and Hapsburgs are facing each other across the disputed borders of the old Duchy of Burgundy, and the Hapburgs are facing off against King Matthais Corvinus of Hungary over Austria.
Lets say that Mehmet II's invasion is very successful, and he takes Rome and is able to co-opt a northern Italian prince (I'm going to make it a Sforza, because this is my post), who they support ala Wallachia. With a solid hold over Naples, Rome, and Sicily he extends Ottoman sovereignty west, over the Barbary States, and Granada. Spanish politics was very divided, in fact the crowns of Castille and Aragon remained seperate for quite a while (and the crown of Portugal was never permanently brought in) so there is a great possibility that Spain breaks into its constituent parts.
IMHO the Moors remaining in Iberia is a massive moral victory. And they have Italy. Maybe the Ottomans extend their sponsorship of Christian princes into Southern France, and their preferred candidate wins one of the wars of succession in Iberia. So they rule by proxy over most of the territory.