One way in which The French Lieutenant's Woman is a postmodern work is that it adopts metafiction as a narrative technique.
As a work of metafiction, which is one of the most important elements in literary postmodernism, Fowles's book is a work of fiction about fiction. What this means, among other things, is that the process of constructing the narrative is every bit as important as the contents of the actual story.
Because of the metafictional technique adopted by Fowles, we are left in no doubt that the novel presents us with illusion rather than truth. A key element of postmodernism is the idea that truth, if not exactly relative, is at least fragmented, making it difficult, if not downright impossible, to construct a truthful narrative that can command universal assent.
By placing a huge wedge between the story and the narrator's metafictional commentary on the story, Fowles freely plays with the postmodernist notion of truth to the extent that the reader is forced to postpone all notions of reality and simply accept The French Lieutenant's Woman as a work of the imagination, which can give us little, if any, insight into what is ultimately real.