Place eggs in a saucepan with enough cold water to cover. Bring to a boil and immediately remove from heat. Cover pan, and let eggs stand in hot water for 10 to 12 minutes. Drain, cool, and peel. Cut in half and remove yolks. Mash yolks with a fork. Slice whites into small pieces.
In a large bowl, toss together the egg whites, iceberg lettuce, romaine lettuce, and leaf lettuce. Arrange the cucumber slices on top of the salad in a ring along the inside edge of the bowl. Sprinkle salad with carrots inside the cucumber ring. Sprinkle all with egg yolks.
In a separate bowl, mix the French salad dressing, creamy salad dressing, and hot pepper sauce. Serve as dressing for the salad.