While the two greatest power of Catholic Christianity, the Quadruple Monarchy and France, were more interested in fighting each other, which culminated in the Great Occidental War, the Empire of the Rum-Seljuks was able to take most of Italy and invade deep into the HRE. This was their apogee, though; now the European powers came to their sense and attacked them, defeating them in the second Occidental-Seljuk War and the first French-Seljuk War. Still, the Seljuks held some parts of Italy and Hungary.
Under the kings Henry V and François III, the two powers had come to an understanding, which became apparent in their agreement to divide Aragon in 1599. At this opportunity, they also decided to deliver a good strike against the Seljuks.
In the peace of Naples, the Seljuks had to give parts of South Italy (Pescara, Benevent) to Florence, the Ionian islands and Crete to Venice, the Sinai to France and core Hungary to Bourbon Hungary under Ferenc I. All of Algeria and Tunisia were left to the Triple Monarchy of England-Castille-Portugal.