In a small bowl, using a fork, beat eggs, crème fraîche, salt, Comté, and fontina until thoroughly mixed, 1 to 2 minutes.
Heat butter in a 10-in. nonstick frying pan over medium heat until it melts and bubbles. Add egg mixture. Very gently stir with a wooden spoon, folding egg curds onto themselves in a figure eight, until they thicken, 1 to 2 minutes.
Decrease heat to low and continue to cook without stirring until eggs are creamy and barely set, 2 to 3 minutes, or another 30 seconds or so for firmer eggs. Spoon onto warm plates, spoon salsa verde on top, and serve parmesan and toasted bread at the table.