Place fennel, onion and garlic in a food processor and pulse to coarsely chop.
Heat oil in a 6-quart heavy pot over medium-high heat, then stir in chopped vegetables, bay leaves, thyme and red pepper flakes. Season with salt and pepper. Cook, covered, over medium heat, stirring once or twice, until vegetables begin to soften, about 4 minutes. Add tomatoes with their juice, broth, wine, and clam juice and simmer gently, partially covered, for 30 minutes. Add clams, grouper and triggerfish and cook a few minutes, partially covered. Add mussels and cook until fish is just cooked through and mussels open wide, 4 to 6 minutes.