I'm not sure "fiction", as we moderns understand the word as a particular type of literature, is an appropriate one for an ancient and diverse anthology such as the Bible. To be sure, a number of its historical claims are suspect, but I fear a label of "fiction" is anachronistic and would prompt dismissal of both its utility as a historical source (one among many from the ancient world) and its transformative potential, quite aside from whether or not one is convinced of its theological claims (and I am not, for the record). Rather than redefining what the compilation is, perhaps awareness of how we approach it is a more fruitful way to conceptualize 'secular' discussion of the Bible.Then, let's discuss the Bible in a secular way.
This is actually an interest of mine (even though I am in no way an atheist). I've always said we should teach the Bible in American schools, but teach it as a secular text of fiction.