Drain the beans and put into a large heavy casserole, preferably enameled cast iron, with bacon, pork rind, garlic, 1 onion, the carrot, and the bouquet garni. Cover with the 10 cups of water and bring to a boil. Simmer over low heat, stirring often, until beans are barely tender, about 1 hour. Drain and return to casserole, discarding onion and bouquet garni.
Add the remaining onion, the duck legs, demi-glace mixture, and tomatoes, and bring to a boil. Add a pinch of salt and pepper, and simmer over low heat for about 15 minutes.
Drain the bean mixture in a colander over a bowl and reserve 5 cups of the cooking liquid. Discard bacon and pork rind. Remove the duck legs and cut each in half at the joint. Season beans with 1 teaspoon salt and a few grindings of pepper.
Preheat oven to 325 degrees F.
Place half the bean mixture in casserole. Add duck legs, duck sausage, and garlic sausage, and cover with remaining beans. Add reserved cooking liquid and drizzle the duck fat over the top. Cover and bake until hot and bubbling, about 2 hours. (Cassoulet may be prepared ahead to this point, then cooled and refrigerated for up to 3 days. If refrigerated, bring to room temperature before proceeding).
Increase oven temperature to 400 degrees F. Uncover cassoulet and bake until top is browned, about 20 minutes. Remove from oven and serve.