Combine the crème fraîche with dill, lemon juice, salt and pepper. Cover and refrigerate the dressing until serving. Season to taste.
Peel the beetroot and core the apple. Thinly slice the beetroot and apple, using a mandolin slicer if you have one, and combine with half the dill, the chopped capers, oil, vinegar, salt and pepper. Arrange the salad in a serving dish and garnish with dill. Serve with the dressing on the side.