French structuralism no longer enjoys the widespread popularity (among critics, intellectuals, etc.) that it enjoyed in the 1960s, but it has made important contributions to literary theory.
Structuralism drew attention both to patterns within texts and to similarities between texts, so one contribution would probably be a closer attention to narrative structures and genres of literary works. New Criticism, which ruled almost uncontested into the 1950s as the primary form of literary criticism, has probably always been better suited to poetry than to prose and viewed texts in isolation. Structuralism works very well with prose, by contrast, and viewed texts in relation to other texts.
Aside from serving as a counter to New Criticism, one of the main contributions that I would identify is the understanding that a structure or pattern (one based on the structure of language) can be uncovered in any sort of system, not just literary texts. The structuralists opened the door wide on what can be interpreted: advertisements, architecture, fairy tales, practices of food preparation, etc. Anything and everything is now a “text” that needs to be read and critiqued.
Structuralism also, obviously, made post-structuralism and deconstruction possible. As early as the later 1960s, many of those same critics and intellectuals who had previously embraced the structuralist belief that a final “truth” could be uncovered through extended analysis of a system (Roland Barthes is a great example!) converted to a poststructuralist views of “truth” as provisional or illusory.
The Wikipedia article (see the link below) gives a good overview. Wikipedia is an interesting and uneven source, so use it (and all sources, I suppose!) with some caution, but the entry on structuralism looks accurate to me.
The term "Strucuralism" appeared in the works of French Anthrolopist Claude Levi-Strauss and gave rise in France to the "structuralist movement" which spurred the works of such thinkers as Louis Althusser, the psychoanalyst Jacques Lacan, as well as being a part of any such movement. Most members of this movement did not describe themselves as being a part of any such movement. Structuralism is closely related to semiotics.
By the early 1960s structuralism as a movement was coming into its own and some believed that it offered a single unified approach to human life that would embrace all disciplines. Roland Barthes and Jacques Derrida focused on how structuralism could be applied to literature.