Set some tarragon leaves aside for the garnish. Chop the rest coarsely and purée briefly along with the crème fraîche, cream, white wine vinegar, some lemon zest, anchovies and capers. Season with salt and pepper.
Dice the potatoes and fry in oil until golden brown, drain on kitchen roll and then season with salt and pepper.
Skin the rainbow trout if necessary. Core the apple, remove the seeds from the chilli pepper and peel the shallot. Then dice everything finely. Mix the fish, apple, shallot and chilli pepper with salt, pepper and olive oil. If you like, add a dash of soy sauce.
Put the tarragon cream on a plate, spread the tartar on it and garnish with potato cubes and tarragon leaves.