Cook the fettuccine pasta according to package instructions until al dente.
While the pasta cooks, heat olive oil in a large skillet over medium-high heat.
Season the salmon fillet with salt and pepper, and add it to the skillet, cooking for about 5-6 minutes on each side.
Remove the salmon from the skillet and let it rest before breaking it into pieces.
In the same skillet, sauté minced garlic until fragrant, about 1 minute.
Pour in the heavy cream and bring to a simmer, stirring occasionally.
Stir in the grated Parmesan cheese until melted and smooth.
Fold in the baby spinach until wilted, and add the lemon juice.
Combine the cooked pasta with the sauce and flaked salmon in the skillet.
Serve hot, garnished with fresh parsley.