Are there any "fake" French words used in English?
Solution 1:
Yes, there's even two sections for different types of these in the Wikipedia article about French phrases used in English ("List of French expressions in English"):
Not used as such in French
Found only in English
I remember reading before that nom de plume is not idiomatic in French, where instead they use nom de guerre. However, it appears that nom de plume now exists in French as well (thanks to Basj for the correction), possibly due to influence from the English term.
Another funny one I vaguely remembered reading about is giclée, a neologism coined to make art printed using an inkjet printer sound fancier, but that has unfortunate connotations of ejaculation in French (it literally refers to a "spurt" or "squirt").
Solution 2:
"Double entendre" is a fake term made of two real French words which is only understood by English speakers and has no real meaning in French:
https://en.wikipedia.org/wiki/Double_entendre#Etymology