Bring a pot of well-salted water to a boil. Cook the bavette until al dente, and drain. While the pasta cooks, roughly chop the oregano leaves and tear the basil by hand.
Heat the oil in a skillet with the garlic and parsley, and add the oregano and basil. Add the mussels, clams, and white wine. Cover with a lid and cook, removing the shellfish as they open and discarding any that don’t open.
Remove them from the saucepan, shell three-quarters of them, and transfer them to a bowl.To the same skillet, add the red mullet, all of the shrimp, and the tomatoes.
Cook, stirring, for a few minutes; the sauce should still be fairly liquid. Add the mussels and the clams. Season with salt and pepper to taste. Transfer the cooked pasta to the skillet with the sauce, cook briefly to meld the flavors, and serve.