In a 6- to 8-quart pan, combine broth, wine, cream, fennel seed, and thyme.
Peel potatoes and thinly slice into pan. Cover pan and turn heat to high.
Trim tops from fennel and save the feathery greens. Trim off root ends, bruised areas, and coarse fibers from sides of fennel. Rinse and thinly slice fennel and add to soup. When mixture boils, reduce heat and simmer until potatoes are very tender when pierced, about 20 minutes.
Meanwhile, rinse feathery fennel greens and chop.
Scrub mussels and pull off beards.
Shell, devein, and rinse shrimp.
Cut seabass into 1-inch chunks.
When potatoes are tender, add mussels. Cover and simmer 3 minutes. Add shrimp and seabass and simmer until mussels open, 3 to 5 minutes more. Ladle into bowls and sprinkle with reserved fennel greens.