Place the chopped shallot, vinegar, zests, juice, olives, fennel seeds, salt and pepper to taste, and oil in small bowl and whisk until well blended. Set aside.
Trim the stalks from the fennel bulb. Snip the greens from the stalks and save them for the salad below. Cut the fennel bulb in half. Using a mandoline, cut the fennel in paper-thin slices. Set aside in a bowl. Cook’s note: If you do not have a mandoline, you can use a potato hand-peeler. Cut the fennel bulb in quarters and shave the bulb starting right across the top and working your way down.
In a large bowl, gently mix the arugula with the fennel. Divide equally in the center of four large plates. Garnish each salad with a few orange and clementine slices. Drizzle with the olive vinaigrette. Top each salad with some Parmesan shavings. Sprinkle with the chopped fennel greens and freshly ground pepper and serve immediately.