I had a job while in university in a temporary customer service type position with the government, and we would get the occasional obviously French caller. I was technically capable of handling the call in French and would always answer them back thusly, but as soon as they heard my accent, they would switch to English
My French accent has improved tremendously since, to the point that I once interviewed for a job at a French school (I am a language teacher) and they pretty much told me 'wow, your French is great for an Anglo, too bad we only hire native speakers.' I took it as a compliment and believe they intended it that way. I pick up languages easily. It's no sweat for me to learn some basic phrases if I'm going somewhere that requires it.