Begin by bringing a large pot of salted water to a boil. Add the 8 ounces of fettuccine pasta and cook according to the package instructions until al dente, usually 10 to 12 minutes. Drain the pasta, reserving about half a cup of the pasta cooking water for later. Set the pasta aside while you prepare the sauce and salmon.
Pat the salmon fillets dry with paper towels. Coat them evenly with 1 tablespoon of Cajun seasoning, making sure every side is well covered. Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Once hot, add the salmon fillets skin-side down if skin-on, and cook for about 4 minutes per side, or until the salmon is cooked through and flakes easily with a fork. Remove the salmon from the skillet and set aside. If you prefer, you can flake the salmon into large chunks once slightly cooled.
In the same skillet, reduce the heat to medium. Add the minced garlic and sauté for 30 seconds until fragrant, being careful not to burn it.
Pour in the chicken broth and heavy cream, stirring to combine. Let the mixture simmer gently for 3 to 5 minutes until it starts to thicken slightly.
Stir in the halved cherry tomatoes and grated Parmesan cheese. Allow the cheese to melt fully into the sauce, which will enrich the texture and flavor. Season the sauce with salt and freshly cracked black pepper to taste. If the sauce feels too thick, use some reserved pasta water to loosen it to your desired consistency.
Add the cooked fettuccine pasta to the skillet with the sauce. Toss well to coat every strand in the creamy Cajun goodness. Gently fold in the salmon pieces, taking care not to break them up too much. Warm everything through for a minute or two.
Turn off the heat and sprinkle the dish with chopped parsley for a fresh, herbaceous finish. Serve immediately, perhaps alongside a crisp green salad or garlic bread for a complete meal.