Peel celeriac thoroughly, removing all rough patches. Cut in half then into thin slices, then julienne into fine matchsticks. Work quickly.
Place in a bowl with lemon juice and toss immediately to prevent browning.
Make rémoulade: combine mayonnaise, both mustards, white wine vinegar, and crème fraîche. Season with salt, white pepper, and cayenne.
Drain celeriac if much liquid has accumulated. Add to rémoulade and toss thoroughly.
Add parsley, diced cornichons, and capers if using.
Taste and adjust — it should be tangy, mustardy, and properly seasoned.
Refrigerate at least 1 hour before serving. The sauce mellows and the celeriac softens perfectly.