^^^^^ Okay, so a sort of half-syllable "uh" at the end, similar in pronunciation to, say, "quatre" or "outre", correct? That does sound right.
And yes, "the rest of the story" would be interesting.
As for a new name for the not-quite-mixte, why does it have to be based on French? The few modern examples I've seen are made by Nishiki and Schwinn, along with bg's Bianchi example.