Madame Verdun is Paul's wife. She does not warm up to Hassan or anyone, and seems super intolerant of Paul, both in his life and his death. When having tea with her after Paul's death, Hassan comments to us that her "old-fashioned way of talking always sounded to me like a deliberate attempt to let Paul's friends know that she was of 'better' stock than her self-made husband" (15.9). So basically she's a snob.
She's sharp tempered, she's shallow, and she doesn't really show any redeeming qualities. By the time her late husband's memorial dinner arrives, she's already got a hot new date: Paul's greatest nemesis, Chef Mafitte. Classy, right? In the end, Hassan kind of just feels badly for her and thinks she's pathetic rather than intentionally horrible.