When native speakers of one language try to reproduce the words of another language, the results will vary naturally and understandably with the linguistic skills of the imitators. In this respect, the speakers of certain languages—Japanese in particular comes to mind—have a deservedly bad reputation for their utter inability to refrain from mangling the vocables of foreign languages. In this respect, speakers of English are somewhere in the middle of the scale of success when it comes to this task.
Speakers whose native language is American English do not, as a rule, fare well with French, despite the ubiquity of French borrowings in English and the frequency of French words and phrases that happen to be intercalated in English utterances as a matter of course. Particularly glaring examples are items that end in –eur in French (like entrepreneur and liqueur), which are typically rendered with the vowel of English pure rather than the more authentic vowel of sir. The latter is certainly within the grasp of an English speaker, who typically mangles the French by modeling their pronunciation on the orthography. Also badly served are words that end in –oir, such as the frequent item noir of film noir, which are regularly distorted by having the final [-r] omitted in utterances containing them by Americans. [ADDENDUM: Cf. the all-too-common mispronunciation in the media (as pointed out to Y-H-B by Jacobus Primus) of the phrase coup de grâce with the final consonant of grâce missing, making it sound ludicrously like gras ‘grease’ instead of ‘mercy’!]
Lately, because of its prominence in world affairs, the designation of the organization of doctors who go by the appellation Médecins Sans Frontières (Doctors Without Borders) comes in regularly for mispronunciation in the mouths of the American media. The first word, Médecins, is actually easy to reproduce, once one knows that the second vowel is elided in French, hence disyllabic and not trisyllabic, and the final vowel equivalent to the nasal vowel of aunt.
The upshot of all this distortion is inescapable, namely the deep-seated idea in the American psyche that FRENCH IS AN EXOTIC LANGUAGE, with a hopelessly wayward phonetics that lies beyond the reach of speakers of American English. Vive la France!