Interesting discussion gentlemen,
The "Frankish" connection seems very intriguing to say the least. I have searched a bit around Slovak sources and found a passage in an on-line article that somewhat reinforces the theory
http://korzar.sme.sk/c/4534059/muzejna-abeceda.html
To paraphrase Jozef Duchoň, an employee of Eastern Slovak Museum ,
" the origins of the term FRINGIA dwells somewhere in the times of the crusades, during which every Christian warrior was reffered to as "Franží" (Franji?), which was a corruption of the word Frank. Naturally the weapon of a Franží was thus called a "Franžíja" (Franjia?). This Arabic term was later on borrowed by the Turks, that succedded in subduing Balkans as well as the majority of the former Kingdom of Hungary. Thus the oriental name for a weapon of european origin came into use in the central europe. The term originaly meant a slightly curved combat saber , that sported a wide blade as well as a pronounced yelmen. The weapon was in use from 17th till 19th century, especially during the anti-habsurg uprisings."
Excuse the somewhat ad hoc translation. Also , I would take the statement with a pinch of salt, as curators (as well as museum employees) tend to sometimes amplify and even invent ridiculous theories in order to catch attention. Theoreticaly speaking though (i.e. when we would take this theory as valid), it doesnt sound that far feched. On the basis of the aforesaid theory , I would assume that the sabres manufactured in the territory of Ottomans were marked with FRINGIA letters , for the purpouse of being shiped to "FRINGIA" , i.e. Christian lands (non-ottoman europe , particulalry Poland and what was left of Christian Hungary+later liberated Hungary), but than again its speculation from my part.
All the best,
Samuel