First, read the Introduction and see how the folk tale and wisdom literature elements are presented. If your students are interested in this, there is a wealth of material for them to use in writing/researching a paper on many of the stories.
Second, in a multi-level class, you can have all the students read the actual Alphonsus story, then have the more advanced students read either the Gesta versions or the other Latin sources that are presented with each story. The less advanced students can read about the wisdom/folk tale origins in English and add their commentary.
You can also have students write their own moral to the story, whether it’s the Alphonsus or the Gesta version.
Second, explain to the students that they now have a chance to understand the medieval mind. Things that we see know are not possible (e.g., a column rising in the middle of the ocean) were perfectly reasonable to the time period. If students look at some of the old maps, they will see lots of fantastic items listed. It’s not that these people were “stupid,” it’s that their understanding of the world allowed the mystic and the real to coexist on the same plane.