In a medium pot, cover potatoes with water; bring to a boil. Cook until tender, about 8 minutes. Remove potatoes. In batches, cook haricots in pot until just tender, about 3 minutes. Transfer to an ice-water bath; drain. Whisk lemon juice, mustard, and shallot in a bowl; whisk in oil, then parsley. Season with salt and pepper.
Bring 2 inches water to a simmer in a shallow saucepan. Season fish with salt; add to water with lemon halves. Cover; turn off heat. Let stand until fish is firm, 8 to 10 minutes. Remove fish; flake into large pieces. Arrange fish, vegetables, and olives on a platter. Season with salt and pepper, drizzle with dressing, and serve.