I've used English for a long time and it isn't immediately obvious to others that I'm native French. Whenever I speak a French word or place name in English I wonder whether I should pronounce it like English or French speakers would. (Of course I always use English pronunciation for common place names like Paris.) Using French pronunciation can sound pretentious, but English pronunciation can too, especially if part of the audience speaks French and knows that I am native French.
This question is similar. My question focuses on native French speakers that speak in English to an audience of both English and French natives. Which pronunciation draws less attention?