Boil a large pot of salted water. Cook linguine until al dente, about 9–10 minutes. Drain, saving ¼ cup of pasta water. Set aside.
Pat salmon dry and season with salt, pepper, smoked paprika, and Italian seasoning. Heat olive oil in a skillet over medium-high. Cook salmon skin-side down for 4 minutes, then flip and cook 3–4 more minutes. Remove and set aside.
In the same skillet, melt 1 tbsp butter. Add shrimp, season lightly, and cook 2–3 minutes per side until pink. Remove and set aside.
Add remaining butter to the pan. Sauté garlic for 1 minute until fragrant. Stir in heavy cream and simmer gently. Add Parmesan and stir until smooth. Let thicken for 2–3 minutes.
Stir in chopped spinach and let it wilt. Add a pinch of Italian seasoning and red pepper flakes if desired. Season to taste with salt and pepper.
Add cooked linguine to the skillet and toss to coat in the sauce. If needed, loosen the sauce with reserved pasta water.
Top the pasta with salmon and shrimp. Spoon sauce over the top and serve warm with extra Parmesan.