Lightly whisk the eggs with the crème fraîche, season with salt and pepper.
Heat the olive oil in a large pan, add the eggs and let set over a medium flame for about 2 minutes. Crumble the goat cheese on the omelette, sprinkle some savory or mountain mint lightly grated over it. Reduce the heat and cover the omelette over a low flame for about 4 minutes.
Serve with fresh baguette or pain de campagne. A green salad or a couple of tomato slices go well with it.