I think this name is pronounced like the word chignon, where the g is silent, almost like saying minion, but the last syllable is pronounced like yawn.To basically put it, min-YAWN. But then again, I could be wrong.
Pronounced mee-nyoh[ng], the [ng] being a nasal sound we don't have in English. (source: I'm married to a Frenchman, and have lived in Paris for almost a decade).
https://en.wiktionary.org/wiki/mignon#French [noted -ed]