In a 5-quart saucepan or Dutch oven, heat the oil over medium-high heat. Add the chicken and season with 1/4 teaspoon of salt and 1/4 teaspoon of pepper. Cook until the chicken is almost cooked through and no longer pink on the outside, 1 to 2 minutes. Using a slotted spoon, transfer the chicken to a medium bowl.
Add the fennel, bell pepper, onion, and garlic to the pan. Season with 1/4 teaspoon of salt and 1/4 teaspoon of pepper. Cook until just tender, about 5 minutes. Add the clam juice, the tomatoes with juices, bay leaves, paprika, saffron, and 1/8 teaspoon cayenne. Bring the mixture to a simmer. Add the spaghetti and cook, uncovered, until almost tender, stirring occasionally, about 9 minutes. Return the chicken to the pot. Bring the sauce to a simmer. Add 1/4 teaspoon salt and 1/4 teaspoon pepper. Add the clams and shrimp. Cover and cook until the clams open and the shrimp are pink and cooked through; 4 to 5 minutes (discard any unopened clams). Remove the bay leaves and discard. Season with salt and pepper, to taste. Mix in the parsley and serve.