The two greatest power of Catholic Christianity, the Triple Monarchy of England-Castille-Portugal and France had defeated the Rum-Seljuks several times in the second Occidental-Seljuk War, the First French-Seljuk War and the Great Seljuk War. Still, the Seljuks held some parts of Italy and the Balcans.
When king François IV had come of age and defeated his inner enemies, he wanted to gain fame and power by striking against the Seljuks too. Triple Monarchy of England-Castille-Portugal had fallen apart at this time already, so he was without competition. So the Second French-Seljuk War took place, during the years 1635-46. Again, smaller powers like Florence and the members of the Alliance des Alpes joined the war at France's side.
In the peace of Györ, Bourbon Hungary acquired Croatia, Slavonia, Transsylvania and the Banat, France the strategically important Aden, Venice the Peloponnes, Florence the northern half of South Italy. The Italians grumbled, however, because they thought their share was too small.
After the fifth defeat in a row, since 1650 Seljuk intellectuals (for the lack of a better word) suggested a different policy - instead of trying to regain a foot in Europe, the Empire should try to build up a "Greater Seljuk Empire", including many areas in Persia and Choresm, like the empire of sultan Saladin.