Like Jules et Jim, the story involves a threesome – here largely over a ten-year period –although in Deux Anglaises (which begins in 1899 and is told in the form of letters and diaries) there are two females instead of two males. Claude is the Frenchman who at first visits the sisters' family, and he decides to ask Muriel to marry him, which she refuses, saying that she'd prefer them to have a brother-sister relationship.
It's actually far more complicated than this, as Muriel is the puritanical, religiously obsessed sibling, and she's very confused about love, fluctuating between loving Claude and not loving him. She sees the Maître-moi of Claude coming to the fore, as opposed to his Vrai-Moi: a simple analysis of the terms would be that Maître-moi is the Freudian superego, Vrai-Moi the id.
Parental guidance decides on a year of the couple not seeing each other, although before the end of this period Claude has decided that he will not marry, although this distresses Muriel, who remains 'faithful'to him, or to her idea of who she is. She also remains faithful to her religion, although she has harboured feelings of guilt about sexual impurity over a number of years: owing to lack of sufficient space one holiday, as an eight-year-old she once spent every night for a week sleeping with a girl of the same age and they had naked cuddles, fondly exploring each others' bodies; and guiltily, Muriel has often masturbated as it helps her to sleep, although she knows that it's, er, harmful.
To cut a long story short, Claude beds both Anne and Muriel, although they both marry someone else, and Claude seems to be left on his own. A novel exploration of the nature of love, whatever that is.