Bring a large pot of salted water to a boil and cook the fettuccine according to package instructions until al dente; drain and set aside.
Season the shrimp with 1 teaspoon salt and 1 teaspoon freshly ground black pepper, then toss to coat evenly.
Sprinkle 1 tablespoon of flour over the shrimp and toss to coat; repeat with the second tablespoon so the shrimp are evenly dusted.
Heat the butter and olive oil in a large skillet over medium-high heat until hot and shimmering.
Add the shrimp in a single layer and cook without crowding, about 2–3 minutes per side, until golden brown; transfer the cooked shrimp to a plate.
Pour the chicken broth into the skillet and cook for about 5 minutes, scraping the bottom to deglaze and concentrate the flavors.
Reduce the heat to medium, whisk in the whipping cream, and cook, stirring, until the sauce becomes bubbly and begins to thicken, about 5 minutes.
Return the shrimp to the skillet, stir in the 1/2 teaspoon Cajun seasoning, and heat briefly to warm through; taste and adjust seasoning with additional salt or pepper if desired.
Toss the cooked fettuccine with the sauce and shrimp until well coated, then serve immediately.
