Heat the olive oil in a Dutch oven over medium heat. Add the garlic and fennel; cook until just soft and fragrant, about 4 minutes. Add the carrots and season with salt and pepper; continue cooking, stirring occasionally, until the carrots are just soft, about 4 minutes. Add the vermouth and boil to reduce slightly. Add the tomatoes and tarragon, then cover the pot and simmer until the vegetables are tender, about 15 minutes. Stir in 1/2 cup water and the mussels. Raise the heat to high, cover and cook until the mussels open, 3 to 5 minutes. (Check halfway through and transfer any open mussels to a serving bowl.) Transfer all the mussels to a serving bowl, discarding any that do not open. Season the sauce with pepper and, if needed, salt, and pour over the mussels. Serve with the bread.