Break the trout into small pieces (either by hand or with two forks), then place in a mixing bowl. Add crème fraîche, chopped fresh tarragon, sliced chive, lemon zest, fresh lemon juice, and black pepper. Use a fork to mash the mixture together until thoroughly mixed.
The smoked trout dip can be enjoyed immediately, but the flavors will intensify as it sits. Store covered in a refrigerator. Just before serving I like to garnish with additional sliced chives and lemon zest.
Serve with sliced baguette, crudité, or in endive leaves!