The description of the fangsong generic font families should include some guidance as to what sort of font it should map to for characters outside of Chinese. If you pick fangsong and write in Latin, or Arabic, or Hebrew, or Thai, what do you get?

I believe the actual expectation is that for languages/writing-systems where fangsong isn't really a concept, the result should be a serif font. At least that seems to be what the Latin part of FangSong fonts tends to look like.