What is the structuralist view of literary criticism, and how has structural literary theory influenced modern approaches to Biblical interpretation?
This is a huge topic. I'll mention a couple things that I'm aware of.
Bruce Benson writes
(Dictionary of Theological Interpretation of the Bible, "Structuralism", Vanhoozer Ed.)
One thing that has come about because of structuralism is the concept of narrative exegesis. The idea is that stories in the Bible (e.g. the Gospels) have a certain structure to them. They contain things like a plot, a protagonist etc. There are differing theories as to what the structures are but that they exist at all come from structuralism. That is to say there is more going on the the Bible than a mere historical report of events.
Another thing that structuralism led to is Post-Structuralsim (as the name implies). Post structuralism emphasizes the cultural side of language. That is to say, each culture constructs their language to work in a certain way. It also provides the meaning to words. Words are not static entities which always have a specific meaning. Rather the meanings of words and texts are determined by the culture that uses them.
Think about the words "gay" and "mouse." The former previously meant happy now it refers to homosexuality. The latter refers to a small rodent (and still does) but I think many people would first think of a computer device when they initially hear the word. Over the past 50 years the chief meaning of these two words have changed considerably in western English parlance. Not because the words changed but because our culture has shifted and now attributes a different meaning to these words
To make along story short. Post-structuralism has challenged the view that there are absolutes that can be drawn from scripture that apply in the same way to every culture and time. The reason for this is that the scriptures as they were written were embedded in a particular cultural and linguistic structure. In order to extract the meaning one must translate from the one culture to our current culture and there is much disagreement on how to do this properly.