Remove skin and bones from fish. Cut into 1 1/2 inch pieces.
Scrub mussels and remove beards.
Trim stems and root end from fennel bulb. Pull feathery leaves from stems and mince. Discard stems and set minced leaves aside.
Thinly slice fennel bulb and combine with onion, garlic, carrot and oil in a 5-6 quart pan over medium-high heat. Stir often until vegetables are browned.
Add tomatoes, broth, clam juice, wine and cayenne. Bring to a boil over high heat; cover and simmer 10 minutes.
Add fish and mussels. Cover and simmer just until fish is opaque but still moist-looking in center (cut to test) and mussels pop open, about 5 minutes. Add minced fennel greens and ladle into wide bowls.