As in "Artist manque" or any other fill-in-the-blank manque. I believe there should be an accent over the 'e', but I don't know how to do that on this screen. My sense is that this means not quite the real thing, but I don't know in what sense. A fake? Someone who aspires to be the real thing? My sense of the word has always hinted at the over-the-top or outrageous, but this may just be a reading into the word...Here goes.
Not too far off. Manque: unfulfilled or frustrated in one's ambitions, as an artist manque, or writer manque. A "would-be" (Is that the same as a wannabe?) Ambitious.
I think I probably conflated outre into my understanding of the word, as it doesn't seem to suggest anything of the outrageous in it. Fake isn't quite right either, but I think I did catch something of the flavor of the word.