What does ménage à trois mean in English?

I don't think ménage à faux-pas exists in French.

Ménage à trois has the same meaning in French and English.

Ménage has several meanings (housework and couple living together mostly )

to set up house with someone = se mettre en ménage.

Un ménage à trois is usually a way to define a couple in which one has a extra in a love triangle.