I'm 1/16 [...]

How prevalent is that, really? I see it all the time from Europeans here on Reddit, especially browsing similar topics in /r/ShitAmericansSay.

I've never heard an American say anything like that, but then again other Americans aren't usually professing their ancestry to me.

I'm Cajun. Our history goes to Canada and to France. We, a lot of us, my family included, speak an old version of French as it might have been spoken in the 18th century and have traditions that date back even further to the 14th century, along with pseudo-belief in old folk tales from feufollet (fairy fire, will-o-wisp) to loup garou. I wouldn't say I'm French nor Canadian, I'm from Louisiana -- it just seems really odd that people would claim a fraction of some place. It would be even stranger to say I'm French -- France has moved on since some of them left France, it's an entirely different country now. It's the same for Scotland, Ireland, Germany.

I don't know what point I'm trying to make, if any. Maybe that it's a stereotype and started somewhere and that it's just so hard to believe people like that exist.