Combine crème fraîche, lemon rind, green onion, chives, flour, egg yolks and half the smoked trout in a bowl and mix to combine. Season to taste with sea salt and freshly ground black pepper.
Whisk eggwhites and a pinch of salt until firm peaks form, then fold into trout mixture.
Heat butter in a 25cm-diameter frying pan over low heat until starting to foam, pour in omelette mixture, gently shaking pan to level. Cook for 1-2 minutes or until base is golden. Scatter remaining trout over half the omelette, place under grill and cook for 1-2 minutes or until light golden. Gently fold omelette in half.
For noisette, heat butter in a small saucepan over medium-high heat for 5-6 minutes or until brown, remove from heat, add lemon segments and chives and combine. Spoon over omelette and serve with baguette and lemon wedges.