"Neighbour" vs "neighbor" is not "old school". One is the correct way to spell it in British English, the other is the correct way to spell it in American English. "Faux pas" comes from French and so is spelled the way it is spelled in French. There's no linguistic mystery, "fopas" is just not a word.
Tell that to spell-checker companies, or at least the Google Chrome team. And UK English is considered "old school" by some, similar to the "old world" versus "new world" labels. But arguing over words and words about words is probably off topic.
