Though the majority of altair pieces and religious paintings from the 15th century europe show the "Turks" armed with wickedly curved falchions , messers and the like , there is an exceptional paiting from Giovanni Bellini. His "Resurrection of Christ" painted 1475-79 shows both a curved sword with a falchionic "clipped point" ( the figure on far left;the feature seems to be also present on some messer pieces as well) as well as a "sabre-proper" ( the figure on the far right) , note the general S profile of the whole weapon. The curved blade , canted hilt , crossguard and (tiny) pommel are reminiscent of the sabres used by Ottomans / Hungarians and various Balkan people during the 15th/ early 16th century.


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As a Venetian, Bellini might have seen a sabre for real , since during the second half of the 15th century a huge number of Greco-Albanian refugees fled from the Balkans and settled in various Italian states , where they served as bordermen / Stratiots. It might not be entirely impossible that the weapon depicted is of Stratioti origin , whose armamanet is described as similar to that of Turks.

Cheers ,
Samuel

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And Bellini was painting Turks. Not Saracens.

Saracen is just a generic term to name all muslems during the crusades, not a specific national group.

12th century manuscripts show the saracens much alike crusaders: chainmail armours and straight swords; the major difference shown is the flags - cross vs. crescent moon.
Manuscripts from the mid-13th century onwards, show the saracens with sabers, though shallow curve, adjacent to the period mildly curved blades. One improtant book I recall is the chronicles by William of Tyre.

Even the Europeans seem to have occasionally appreciated a distinction between Arabs, Syrians, Egyptians, etc. ("Saracens" proper for some authors) and Turks. Probably the ones who had learned from Byzantines about the difference in military habits between Arabs and Turks. "Saracens" with straight swords are usually intended to represent the warriors of the Middle Eastern Muslim principalities proper, who did mostly carry straight swords until well after the end of the Crusades, whereas the Turks used all manners of straight, curved, and slightly-curved blades early on, though the image that tends to stick with them is the one with the curved blade because they obviously made more use of curved swords than the Egyptians and Syrians and what-have-you.

Now that I think about the Bellini paintings again, though, I notice that it might not really matter whether he was depicting Arabs or Turks, since by the time he painted those stuff the Turks had conquered most of the Middle East anyway and their fashion were already beginning to widely replace the native panoplies with straight swords and all.