I'm sorry if I'm beating a dead horse here but, again, the name Franjo is not particularly Serbian. This is not in any way a nationalistic proprietary claim on it, it is simply a matter of fact, whether we talk about actual usage, history of the name or, yes, popular perception. I would suggest two particular problems are involved here, though: FIRST, that Francis in general (in whatever form, Franja or Franjo, etc.) is not a very traditional Serbian name (Serbs being Orthodox Christians) and is therefore rare among them to begin with; but that SECOND, notwithstanding the former, we can automatically 'borrow' and label as Serbian that form of the name which is extensively used by neighboring people (Croatians) whose language, by the way, is practically the same as Serbian (let's call that Serbo-Croatian) anyway? The problem with this kind of reasoning (whatever you may think about the relationship between Croatian and Serbian languages), is that proper names, being primarily cultural elements, do not necessarily or simply 'follow' mere language patterns. If that were the case, you might as well entirely abolish distinctive labels Croatian, Serbian, Bosnian and stick with 'Serbo-Croatian' alone. By the way, I see that the latter still survives as an umbrella term and arch-directory on this site for names "used in Serbia, Croatia, and other parts of the former Yugoslavia" (to be sure, Slovene and Macedonian names are not included, so the site is adhering to a simplistic linguistic principle even while not saying so; why else would an obsolete geographic term 'former Yugoslavia' be used?). Regarding my original point about Franjo, a recent event in Serbia may prove instructive: when pope Francis was elected, the Serbian public and media, TV stations, newspapers, and public officials, were very much unsure what to call him: is it to be Franjo (Croatian version, and the one used by Catholics in Serbia), Franja (archaic Serbian version), Franciskus (Latin), Francisko (Spanish or garbled Latin) or even Frančesko (Italian)? In the end public consensus seems to have settled on Franja, since it is undoubtedly Serbian (unlike Franjo) and because it was, without hesitation, used for the pope by the Serbian Orthodox Church.
Not being negative or anything, but I'm positively sure this name is actually very rare in Serbia and among Serbian people. If anything, Franja is the form used in Serbian (although likewise rare), but Franjo at least simply isn't among popular Serbian first names. Unless historical usage (as with Stjepan) or language affinity are considered reason enough, contemporary Serbian and Croatian usages should clearly be discriminated between.
Regarding my original point about Franjo, a recent event in Serbia may prove instructive: when pope Francis was elected, the Serbian public and media, TV stations, newspapers, and public officials, were very much unsure what to call him: is it to be Franjo (Croatian version, and the one used by Catholics in Serbia), Franja (archaic Serbian version), Franciskus (Latin), Francisko (Spanish or garbled Latin) or even Frančesko (Italian)? In the end public consensus seems to have settled on Franja, since it is undoubtedly Serbian (unlike Franjo) and because it was, without hesitation, used for the pope by the Serbian Orthodox Church.