As for travelling outside Canada...
Initially in my youth I travelled as a "French Canadian" (but *not* from Quebec if the conversation got that far). For a couple of decades now I've been more identified to Quebec though - it fits more cleanly into perceptions people have.
For the most part, pretty much anywhere I've been Quebec/French Canada is viewed as an interesting curiosity by the vast majority of people.
In a few cases I've been able to tell that Quebec bashers/anti-French people from Canada had passed through there before me, as people would immediately view me as a shit disturber and ask me all sorts of ignorant stuff that they couldn't possibly have come up with themselves living where they did - especially before the age of the Internet.
But by and large the image we seem to have is that of the quirky outlier, the valiant resister - maybe a tad anachronistic but still worthy of respect.
Of course the reception in the Francophonie (especially in France) is a bit different, though it's very much along these same themes, only hyped up a few notches.
In France you sometimes get the "cousins from overseas" spiel, from people who obviously aren't related to you at all. You'll also get the brave besieged "village gaulois" imagery (as per the Astérix series of comic books).
That's us up there in the top left corner.