This paper is a psychoanalytic study of "gender myths" as presented in John Fowles's famous novel The French Lieutenant's Woman (1969). It begins by describing Fowles's interest in Freudian psychoanalysis and his use of psychoanalytic ideas in constructing fictional characters. The paper subsequently explains how the concept of "postmodern indeterminacy" as found in Fowles's text needs to be read in connection with the "enigma" as embodied by Sarah Woodruff, the female protagonist. An attempt is then made to make sense of the "enigma of femininity" a critical concern among the psychoanalysts. Elaborating on Lacanian developments and critique of Freudian ideas, this paper uses the psychoanalytic notions related to the truth of the feminine, fictionality of the masculine, jouissance, and sexual non-rapport to offer an analysis of the enigma of Sarah Woodruff, the failures of Charles Smithson the male protagonist, and the inconclusiveness of Fowles's narrative. The discussion highlights the link between feminism and Lacanian psychoanalysis on the question of construction of gender identities.