I also don't understand why Claire stays with Laurent. She doesn't strike me as the gold-digger type or the fame-whore type. I'd love to know what he's like in real life. He comes across as being a big, fat, gross lunatic.
Claire knew what she was getting into when they married. I remember her saying that it definitely wasn't love at first sight when they met. I wondered back then why she married him. They seemed like an odd pair. I thought she could do better. And I don't necessarily mean richer.
Laurent is the same person he was when they married. Claire stays because this is a very Catholic family. I know in this day and age, it's easy to get up and leave, and staying when you're disillusioned or out of love with a partner might be hard to understand. But I think she takes her wedding vows seriously. Unless Laurent is abusive or unfaithful (and I don't think he is), there really isn't a compelling reason for her to leave in light of her commitment to her faith and to her marriage and the fact that she knew what she was getting into when she married.
Also, they don't look miserable together. Maybe not "in love", but not miserable. Unlike that couple in Denmark.