I think if I were to travel outside the US these days I'd carry a backpack with a Canadian Flag on it.
I was amused in my trips to France at how attuned Parisian ears are to flavours of English. Certainly people I knew had no problems telling Australians from New Zealanders, and Welsh and Scots from English. This was even funnier when one of my Scottish friends was able to gabble away in French as she went around, whilst my English friends almost always were replied to in English. No matter how fluent their French.
And (of course) when I was going around the US, it was evens as to whether people picked me out as British or Australian for the first week. Then my sponge ear kicked in. (One reason why I can't spend too long in Liverpool 😀)
Anyway, I imagine quite a few French folk won't be fooled by a flag.