Let's say a language uses two vowels /A/ and /B/ which differ only by one relevant phonological feature [+/- X] such that /A/ is [- X] and /B/ is [+ X]. Now let's say there's a consonant phoneme /C/ which is also [+ X]. Finally, let's say there's a phonological rule such that all vowels in the environment of /C/ may be realized phonetically with [+ X]. In this language, how do we phonemically analyze a sequence that includes a vowel phone sharing the features of /B/ preceding /C/? Are /BC/ and /AC/ equally valid analyses?
To make this a like less abstract, the confusion that prompted this question is nasal vowels in languages like French, but it's probably applicable to many other languages and possibly other phonological features. I'm really thinking of /A/ as /ɛ/ and /ɔ/, /B/ as /ɛ̃/ and /ɔ̃/, and /C/ as /n/ and /m/. I know that it's super common in world languages for vowels to be realized [+ nasal] before consonants that are [+ nasal], and I believe this may be true for French as well. Thus, /ɛn/ could be realized [ɛ̃n], which would be same realization as hypothetical /ɛ̃n/. If this is true, we have to either say: 1) that the distinction [+/- nasal] is neutralized for vowels before /n/, or 2) that /ɛ̃/ is not allowed to occur before /n/ (making /ɛn/ the right analysis of [ɛ̃n]). What justification is there (French-specific or otherwise) for choosing one claim over the other? Additionally, if claim 1 is chosen, what justification is there for choosing one phoneme symbol over another in transcription?
For example, there is a word pair "chien" and "chienne." I would have assumed that these words only differ phonologically by the presence of /n/ in the latter (and if the next word begins with a vowel, there would be no difference at all due to liaison.) However, I noticed that online resources actually transcribe "chienne" with ⟨ɛ⟩ rather than the ⟨ɛ̃⟩ used for "chien," which strikes me as very bizarre. Either the transcribers are choosing claim 2 or are choosing claim 1 and have some justification to prefer the symbol without the diacritic. As I'm not an expert in French phonology, I'm not sure what this justification might be - it could either be for simplicity's sake (people don't like to use diacritics), for diachronic reasons, or for psychological reasons (which would be by far the most interesting).