Cook the fettuccine pasta according to package instructions until al dente. Drain and set aside, reserving 1/2 cup of pasta water.
In a large skillet, heat the olive oil over medium heat. Season the salmon fillets with Cajun seasoning, salt, and black pepper.
Place the salmon in the skillet and cook for about 4-5 minutes on each side, or until cooked through and flaky. Remove the salmon from the skillet and set aside.
In the same skillet, add the heavy cream and bring to a simmer. Stir in the cherry tomatoes and spinach, cooking until the spinach is wilted, about 2-3 minutes.
Flake the cooked salmon into bite-sized pieces and return it to the skillet. Add the cooked fettuccine and toss everything together. If the sauce is too thick, add reserved pasta water a little at a time until desired consistency is reached.
Stir in the grated Parmesan cheese until melted and well combined.
Serve immediately, garnished with fresh parsley.