Cut off the top and bottom of the celeriac, then peel the rough outer skin with a sharp knife. Julienne into thin matchsticks using a mandoline, julienne peeler, or box grater, tossing immediately with half the lemon juice to prevent browning.
Sprinkle the julienned celeriac with the kosher salt and toss thoroughly. Transfer to a colander set over a bowl and let rest for exactly 30 minutes.
While the celeriac rests, whisk together the mayonnaise, Dijon mustard, crème fraîche, remaining lemon juice, and white wine vinegar in a large bowl until smooth. Season with black pepper.
After 30 minutes, press the celeriac firmly against the colander to remove excess liquid, then pat thoroughly dry with a clean kitchen towel.
Add the dried celeriac to the dressing and toss until every strand is well coated. Taste and adjust seasoning as needed.
Fold in the chopped parsley, cover, and refrigerate for at least 1 hour before serving. Toss once more just before serving.