In a 3-1/2- to 5-quart slow cooker, combine carrot, onion, and sweet pepper. Add drained beans, chicken, sausage, and bay leaf. Sprinkle with parsley, thyme, cayenne pepper, and garlic. In a small bowl, stir together undrained tomatoes, broth, and wine. Pour over chicken mixture.
Cover and cook on low-heat setting for 7 to 8 hours or on high-heat setting for 3-1/2 to 4 hours. Discard bay leaf. Makes 6 to 8 servings.