1Place the crème fraîche and zest in a small bowl and stir to combine. Season with lemon juice, salt, and pepper as desired; set aside.
2Place the eggs in a medium bowl and beat with a fork until broken up. Season with a pinch each of salt and pepper and beat to incorporate. Place 2 tablespoons of the eggs in a small bowl; set aside.
3Heat a 10-inch nonstick frying pan over medium-low heat until hot, about 2 minutes. Add the butter to the pan and, using a rubber spatula, swirl until it’s melted and foamy and the pan is evenly coated. Pour in the larger portion of the eggs, sprinkle with 1 tablespoon of the chives and 1 tablespoon of the tarragon, and let sit undisturbed until the eggs just start to set around the edges, about 1 to 2 minutes. Using the rubber spatula, push the eggs from the edges into the center. Let sit again for about 30 seconds, then repeat pushing the eggs from the edges into the center every 30 seconds until just set, for a total cooking time of about 5 minutes.
4Add the remaining 2 tablespoons raw egg and stir until the eggs no longer look wet. Remove from the heat and season with salt and pepper as needed.
5Divide the reserved crème fraîche mixture among the toasted English muffin halves and top each with a slice of smoked salmon and then a quarter of the eggs. Garnish with the remaining chives and tarragon and serve warm.