Whisk the crème fraîche into the sauce and season to taste with salt. Set the sauce aside to cool to room temperature.
Ladle a thin layer of room-temperature sauce onto the bottom of a 9-by-13-in baking dish. Spread the sauce with a spoon to cover the surface of the dish. Add a layer of 3 sheets of pasta. Spoon over just enough tomato sauce to cover the pasta and then scatter over some of the Parmesan, mozzarella, and basil. Repeat the layering process until you’ve used up all of your components (4 layers of noodles; I do one layer with the lasagna vertically as pictured, the next horizontal, breaking the third piece in half). End with sauce and cheese (not naked pasta or basil, both of which would burn if exposed).