think of the word "wine"

The sound the WI makes finished with a barely perceptible exhaled middle-of-the-mouth vowel sound.

Hmm, assuming you're talking about how an anglophone pronounces wine, the vowel is really a diphthong: /'wajn/. I guess the vowel is a little like the i in tin, i.e., /'tɪn/. Is the sound of the Quebecker yep, like the wi in wit? Or something else? Is there a standard French word that this vowel sound occurs in?

Ceci n'est pas un seing.