Remove the green fronds from the fennel and set aside. Cut the fennel in half and using a mandoline slice into thin slices. Place in a bowl with ice cold water to keep crisp.
Slice off the top and bottom of the blood oranges and place on a cutting board. Slice along the shape of the orange from top to bottom cutting the orange peel away. Then cut the orange into thin round slices and set aside.
In a bowl combine the whole grain mustard, lemon juice and add salt and pepper. Whisking, drizzle the olive oil into the bowl and continue whisking well. Adjust the seasoning with salt and pepper if needed.
Strain all the vegetables and squeeze out any remaining water. Place the fennel, onion and radish in a bowl and pour the dressing on top. Now add the olives, parsley, fennel fronds and oranges and toss lightly. Serve in a bowl or as a side.