I assume your thesis needs to be argumentative / persuasive, which leads me to ask what sort of argument you wish to make. A good place to start is in finding a question about the text (pertaining to betrayal, of course).
She focuses on betrayal a great deal, so your question--a point that interests you, preferable, because an essay written to answer a question that interests you tends to be interesting, in turn, to read--could focus on the overall message or on a single lay, such as "The Chatelaine of Vergi" (Part XVII). This lay is riddled with betrayals, but they generally aren't willing betrayals. The Duchess hits on the knight and, when he spurns her advances, she's hurt and angry, so she tells her husband a lie about him. The Duke initially believes her, but gives the knight the opportunity to prove him wrong, but the knight is now in the bad position of being banished from the dukedom (where he'd never see his lover again) or betraying her confidence, so he makes the Duke promise to never tell another person. The Duke betrays him because his wife pretends to be heartbroken that he doesn't trust her, then uses the information to get her revenge on the knight by telling his lover what she knows. Three people die and we feel a bit sorry for the Duke, but in reality, he was forced to betray the knight in the same way he had forced the knight to betray his lover.
We can see from this single lay that betrayal isn't necessarily a black and white affair; it has many nuances. A good question to guide your essay, were you to focus on this lay, might be, "What is the nature of betrayal in 'The Chatelaine of Vergi'?" The answer to that question would be your thesis (your main claim). (Example: "In 'The Chatelaine of Vergi,' Marie de France demonstrates how betrayal is not a clear-cut affair.")