For a three-act plot analysis, put on your screenwriter’s hat. Moviemakers know the formula well: at the end of Act One, the main character is drawn in completely to a conflict. During Act Two, she is farthest away from her goals. At the end of Act Three, the story is resolved.
Act I
Custance goes to Babylon to marry the Sultan, but finds herself cast out to sea in a rudderless boat by his scheming mother-in-law. Hey, stuff happens.
Act II
Washed up on the shores of Northumberland, Custance is taken in by a kindly Constable and his wife. When a treacherous knight accuses her of murder, she meets the King of Northumbria, who marries her after helping her to clear her name.
The king's mother, unhappy at her son's marriage, arranges to have Custance abandoned at sea again. There, Custance meets the boat of the Senator of Rome, who takes her and her son under his care. So, you know, things could be worse.
Act III
The King of Northumbria travels to Rome on pilgrimage. There, he reunites with his wife and son. He and Custance travel back to Northumbria. After the king's death, Custance returns to Rome and ends her life in piety and almsgiving. Which is a happy ending for her.