Is Jerusalem of Cosmopolitaine culture? I think it shouldn't be... considering that its founders were mainly lords of Frankish (not French), Visigothic, Normand and Lombard descent...
Godfrey de Bouillon was probably Frankish, lord of an area quite germanized by Flemish culture. Raimon de Tolosa was of Visigothic ancestors, lord of Occitan lands, nothing to do with French cosmopolitaine, or even Frankish. Bohemon de Taranto was a Normand, son of Robert Guiscard, the Normand conqueror of Sicily (a Viking, in simple words). Robert de Flandres was Frankish, and Flemish. The House of Montferrato is of Lombard origin...
Crusaders came from everywhere. Even king Sigurd of Norway went on Crusade, and he was the first king to do it, before the Second Crusade. Many lords in the First Crusade came from France, but of course France was not today's homogeneous France. Not at all. And the most important of them came from frontier or outside duchies (Lorraine, Flanders, Boulogne, Normandy, Apulia, Toulouse, Catalonia, Genoa), and knight from everywhere kept coming with their troops.
Maybe cosmopolitaine is not the best option, but which one is left? I'm afraid it's gonna be cosmopolitaine...