Line a baking sheet with foil and set your oven rack a few inches from the broiler. Pat the salmon fillets dry, rub them with olive oil, and season generously with salt and pepper. Broil skin-side down for 4 to 8 minutes until the fish is just about cooked through, since it will keep cooking a bit as it rests.
While the salmon broils, drop your fettuccine into a large pot of well-salted boiling water. Cook it about a minute short of al dente, stirring now and then so the noodles don't clump together. Before draining, scoop out a cup of that starchy pasta water you'll want later for the sauce.
In the now-empty pasta pot, melt the butter and sauté the shallot and garlic with a pinch of salt until soft and fragrant. Pour in the heavy cream and Dijon mustard, then let it bubble gently for about two minutes until it thickens slightly. This is where the sauce really comes alive.
Toss the drained pasta, spinach, and a splash of reserved pasta water into the sauce, tossing constantly until the spinach wilts and everything is glossy and coated. Turn off the heat, stir in the lemon zest and juice, then taste and adjust the seasoning. Pile the pasta onto a platter and break the broiled salmon into big chunks on top, leaving the skin behind on the tray.