In a small bowl, stir together mayonnaise, creme fraiche, cornichons, parsley, lemon juice, capers, mustard, tarragon, and salt and pepper, to taste until combined well.
In a large saucepan of salted boiling water, cook celery root 2 minutes. Drain celery root in a sieve and refresh under cold water. Dry celery root completely. Add celery root to sauce and stir together. Chill salad until ready to serve.