Prep and sauté the veg - Trim the stem and root ends from the fennel. Thinly slice the fennel bulb, reserving the stems and fronds. Peel and dice the onion. Peel and mince the garlic. Wash and trim the carrot, then cut into a small dice. Heat the oil in a large soup pot, then add the sliced fennel bulb, onion, garlic, and carrot. Cook over medium high heat until the vegetables are very soft and beginning to caramelize. While the veg is sauteing, cut the fish into large chunks, then pull the fronds from the fennel stems.
Build the broth - Add the potatoes, tomatoes, broth, clam juice, wine, cayenne and tarragon. Bring to a boil, then lower the heat. Cover and simmer until the potatoes are tended, about 20 minutes.
Finish - Add the fish and the shellfish. Cover and simmer until the fish is opaque and cooked through, and the shellfish have popped open. Remove from heat. Ladle into wide bowls, drizzle with olive oil and garnish with the fennel fronds.