User:Ghoti/English is not French

When we speak a language we always use the phonemes of that language, even if we are saying loanwords. For example, élite in English is /eɪˈliːt/ or /ɪˈliːt/ and not [elit] (besides, the normal spelling is "elite", without acute accent). Similarly football in French is pronounced [futbol] and not (similar but different vowels). This is more obvious in words that share a common origin (i.e. they are loanwords from Latin or another language). For example nation is in English and  in French, and practically nobody uses the French pronunciation when speaking in English or the other way around.

If you speak French you should remember that English is not French, particularly in names of cities, movies, and concepts that don't exist in English (such as bouillabaisse or gendarme). This works also when using English names or concepts in French, like when you say je suis allé à Washington or j'ai bu un milk-shake).

Best shot
Ideally a word should have the best possible adaptation, but not better. For example, good adaptations of the pseudonym "Le Corbusier" are and  The correct French pronunciation [lə kɔʁbyzje] sounds artificial and should not be used in an English conversation.

With reduced vowels
The best shot for bouillabaise is /buːjɑːˈbes/. However the real pronunciation doesn't sound so foreign: /ˌbuːjəˈbeɪs/. Anglicised words have /ə/ or /ɪ/ in unstressed syllables. Note that in this case /ˌbuːjəˈbes/ would have been (arguably) better.

Distorted words
Sometimes words are distorted, either because their pronunciation is difficult or because they are pronounced according to different rules (e.g., spelling pronunciation). For example, in American English the word "lingerie" (French [lɛ̃ʒʁi]) is pronounced /ˌlɑːn ʒəˈreɪ/, which is very different because of pseudo-French pronunciation. In British English a better adaptation is used /ˈlænʒəriː/. The best shot would be /lenʒəˈriː/

Accepted pronunciation and less common words or proper names
If a word is common it will have an accepted pronunciation. For example, the word "café", sometimes spelled "cafe" has the standard pronunciations /ˈkæfeɪ, kæˈfeɪ, kəˈfeɪ/. Pronouncing (best shot) or  (native pronunciation) would sound pretentious. Less common names or words (for example, your own name, or the name of a typical dish) can be pronounced with a best shot. If you are a native speaker of French the native accent will not sound pretentious, but you might not be understood (as shown in the external link).