This is more of urban legend that may somewhat hold true in tourist-heavy areas.
I’m French, this is definitely not an urban legend, for some unknown reason « wrongly » spoken French sounds especially grating to me and all the other French people I know. We might not say it to your face , but it is extremely hard to ignore.
I wonder if it’s the same with other Latin languages, or if it is just some consequence of years of forced standardisation of the French accent.
Weird, I'm French and most people I know are rather delighted to hear foreigners speak French. We have quite a few English pensioners living around where my family lives, and I live myself along the Flanders/Wallonia border in Belgium so we're quite accustomed to hearing "bad French" speakers I guess, but the popularity of foreign speakers singing in French seems to indicate that foreign accents isn't really a problem for many French speakers.
People being annoyed at bad French is stereotypically Parisian to me.
I would assume it's grating for anybody to hear their mother tongue butchered. More so when both sides know they could just switch English and have an adult conversation instead of struggling to buy a loaf of broad and a bottle of water. I always feel the urge to switch and have to remind myself that the other person is making a big effort on their side and that should be appreciated and respected.
P.S. My mother tongue is Spanish and it's many accents are anything but standardized.