Rinse the half fennel bulb thoroughly under cold running water and cut out the hard core. Slice the fennel bulb with a sharp knife or mandoline into very thin slices. Remove the peel from the half orange and cut the flesh between the membranes to get neat segments. Catch any released orange juice in a large bowl.
Open the can of sardines and drain the olive oil, but keep a small splash to use as dressing. Add the finely sliced fennel and the orange segments to the bowl with the caught juice. Mix everything together well. Pour the reserved splash of oil from the sardine can in to season the salad and mix again.
Gently lift the sardines out of the can so they remain as intact as possible. Place the fish on top of the prepared fennel salad, or break them into coarse pieces and gently fold them through. Finely chop the handful of parsley with a chef's knife and sprinkle evenly over the salad.
Distribute the salad over a plate or shallow bowl. Make sure the sardines and orange segments are visible and nicely spread over the paper-thin fennel. Serve immediately.