Beat the eggs in a bowl with the crème fraîche, salt and pepper.
Heat the olive oil in a large pan, add the egg mixture and let it set over a medium flame for about 2 minutes. Spread the salmon on the omelette and sprinkle with the chives. Reduce the heat and cover the omelette for about 4 minutes over a low flame. Serve folded on a platter with a green salad.
Fresh baguette or pain de campagne goes well with it.