Mix in a bowl, French dressing, mustard, tarragon and parsley, beating well with a fork. Add the beetroot, rice and onion to the dressing and, using two large spoons, toss the salad in the dressing. Place the bowl in the refrigerator overnight.
The following day, put the apple in a bowl and sprinkle with lemon juice. Add the asparagus and mayonnaise and stir well until the ingredients are thoroughly blended.
Remove the rice mixture from the refrigerator and pour the mayonnaise mixture on to the rice mixture. Toss the salad, using two spoons. Transfer the salad to a chilled serving bowl and garnish with the slices of hard-boiled egg and parsley sprig. Serve immediatly.