1. To prepare soup, melt butter in a large saucepan over medium-high heat. Add squash, carrot, and onion; sauté for 12 minutes. Add chicken broth, and bring to a boil. Cover, reduce heat, and simmer for 30 minutes. Remove from heat; stir in half-and-half and salt.
2. Preheat broiler.
3. Place squash mixture in a blender. Remove center piece of blender lid (to allow steam to escape), and secure blender lid on blender. Place a clean towel over opening in blender lid (to avoid splatters). Blend until smooth.
4. To prepare toasts, arrange French bread on a baking sheet. Broil for 1 minute or until lightly toasted. Turn bread over, and top evenly with Swiss cheese. Broil for 1 minute or until bubbly. Serve toasts with soup.