"Across the Bay."
Similar in theme to the 1951 novella The Grass God, this story depicts a vacationing veteran's involvement with a young French woman, until he learns that the "father" who joins her each weekend is in fact maintaining her as his lover. The story was dramatized by Gregory Evans for BBC Radio in 1986 in a production starring David Yelland and Juliet Hammond. In Argosy (November 1952), The Daffodil Sky (1955), Seven by Five/The Best of H.E. Bates (1963).
Online Full Text at Hathi Trust Digital Library.