I would think of using 'Frenchie' to refer to a person as being affectionate banter. Like 'Yank' for Americans or 'Canuck' for Canadians. It's not incorrect, but would be inappropriate outside of an informal context.
French people have 'rosbif' to refer to the English and Australians have 'pom' or 'pommie'. You wouldn't call the prime minister that at a diplomatic event, but it's not offensive to call your friends that.
> I would think of using 'Frenchie' to refer to a person as being affectionate banter
Not sure about other English-speaking countries but I'm fairly sure we don't use that word in England. It's exclusively the dog. We usually call them a frog which is quite derogatory, or use a certain tone when saying e.g. "he's French" (implying "ugh"). We also don't call Canadians Canucks but certainly call USAians we dislike Yanks
We English don't really do affectionate banter with the French. We either like/admire them or hate them lol
I mostly admire them, for the record (but it can be testing at times – we find their arrogance quite annoying ;)
French people have 'rosbif' to refer to the English and Australians have 'pom' or 'pommie'. You wouldn't call the prime minister that at a diplomatic event, but it's not offensive to call your friends that.