Peel the oranges and divide into wedges (do this over a bowl, keeping the juice flowing down).
Place the fennel and orange wedges in a large bowl. In a small bowl, combine 2 tablespoons of reserved orange juice, fennel greens, 1 tablespoon olive oil, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Whisk lightly. Pour over the salad with this dressing, mix.
Heat the remaining 1 tablespoon olive oil in a large skillet over medium heat. Sprinkle the fish with the remaining salt, pepper, and thyme. Place fish in skillet and fry until tender, about 4 minutes on each side.