Adventure
If the Sultan and the Emperor of Rome had gotten their way, the "Man of Law's Tale" would be a family drama or a romance. It would be a story in which a beautiful girl marries a worthy man, starts a family, and lives happily ever after, furthering the aims of two dynasties in the process.
Thanks to the Sultan's scheming mother-in-law, however, Custance gets cast out to sea in a rudderless boat, turning the "Tale" into what definitely qualifies as an adventure. For Pete's sakes, she's literally lost at sea.
Tossed by the "wilde wawes," then washed up on a foreign shore, Custance endures all manner of suffering (false accusation, attempted rape, etc.) until finally, she's picked up by a Roman senator on his way home from sacking Babylon. If that's not an adventure, we're not sure what is.