Add the potatoes to a pot and cover with cold water. Bring to a boil and simmer until tender, about 5 minutes. Remove with a slotted spoon (let the water continue to boil) and let cool slightly.
Prepare an ice water bath. Add the haricot verts to the boiling water, blanch briefly and transfer to the water bath to stop the cooking process. Drain, then cut into 2-inch pieces. Slice the potatoes 1/4 inch thick.
Arrange the lettuce on a platter. Top with separate mounds of the potatoes, haricot verts, tomatoes, eggs and chicken, then drizzle with the Mustard Vinaigrette. Season all with salt and pepper. Garnish with the olives.
In a mixing bowl, combine the oil, vinegar, mustard, garlic and shallot. Whisk until emulsified. Season with salt and pepper.