Turn the heat to medium-high. Deglaze with the citrus juice-zest mixture and cook until the liquid has evaporated. Add the dried fruits and chicken stock, and bring to a boil. Turn down to a simmer and gently place the duck legs, skin side up, back into the Dutch oven, making sure they are completely submerged in the liquid. Place the carrots on top and cover the Dutch oven. Either turn the stove top to the lowest heat or place in a preheated 300 degree oven for 2 hours. After 2 hours check to see if the duck legs are so tender that the meat easily begins to fall off the bone. If they are not yet tender, cook for an additional 20 to 30 minutes.