The English equivalent to ménage à trois is quite simply ménage à trois. The OED lists it under its entry for ménage, where it says it means:
an arrangement or relationship in which three people live together, usually consisting of a husband, his wife, and the lover of one of these.
I’m not sure that definition necessarily covers all modern situations, considering that there are many unmarried persons living together. Also, there may be some notion that all three are equally lovers of each other, not just a two-to-one scenario.
You might get away with threesome, but that more often applies more to one given intimate encounter than it does to when everyone is living together intimately.