Wash and dry the beet greens and stems. Slice stems into 1/2" pieces. Thinly slice beet greens and parsley leaves. Using a box grater or the shredder disc of a food processor, grate the beet and celery root.
Combine the mayonnaise, creme fraiche, mustard, lemon juice, and salt in a large bowl. Add black pepper to taste, whisk together and set aside.
Transfer the celery root and beets to the mayonnaise mixture. Add the parsley, beet greens and stems and toss to coat. Season to taste with salt and pepper and serve.