In standard American English, FOY-er is the more common pronunciation, but is often derided by speakers of standard British English, among whom FOY-yay is standard. My survey indicated, unsurprisingly that FOY-er is primarily an American pronunciation, but also that some Australians pronounce it this way too. No Canadians or Brits chose it, however. FOY-yay was chosen by a minority of American respondents, most Canadians and Brits, and a few others. The French pronunciations (regardless of stress) were chosen by a couple of Americans and a substantial minority of Canadians. As always, there were a couple of exceptions here and there.
Like debacle, foyer came into English only in the mid-19th century (1859), through French, which at the time exercised an important influence on English elite culture. We might expect, then, that it would be less than fully anglicized. Indeed, the French pronunciation [fwaje] (fwa-yay) is fairly uncommon. But in the most common pronunciation, FOY-yay, what we see is an incomplete anglicization, not to the expected FOY-er, but instead an anglicization only of the first syllable. In English, [fw] is not a standard onset cluster; without getting into too much English phonology, as a general rule, any English consonant that can combine initially with [l] does not regularly combine with [w], and vice versa (e.g., flee but not *fwee; twee but not *tlee). Thus, most English-speakers adjust [fwaje] to something close and yet acceptable (the 'o' is a nice rounded back vowel that gets you close to [w]). Some (as in Standard American) take yet a further step and pronounce the word with the [r] at the end. (Ironically, speakers of non-rhotic dialects will then abandon the [r] and pronounce it something like FOY-uh). Only a few retain a more purely French pronunciation with initial [fw], but in doing so they are doubtless aware, at least subconsciously, that it is a foreignism.
Foyer, being a recent loanword, is in the midst of a phonetic shift. Interestingly, because the shift is incomplete, the common pronunciation FOY-yay has no full rhymes in English. Obviously, in its standard American form, it rhymes well with lawyer, sawyer, etc., although perhaps not fully, depending on how you pronounce 'aw' in your dialect). Strangely enough, however, a couple poll respondents indicated that they were abandoning or had abandoned FOY-er after hearing FOY-yay or learning that it was 'correct'. So it may in fact be that FOY-yay may not be simply an intermediate form on its way out, but may eventually replace the more fully anglicized FOY-er. No doubt issues of elite culture and language are implicated in this choice, as are American vs. British language issues. It just goes to show you that predicting linguistic change is a tricky business.
