Bring a large pot of salted water to a boil and cook the fettuccine according to package directions until al dente. Drain and set aside, reserving a little pasta water if desired.
In a bowl, sprinkle 1 tablespoon Cajun seasoning over the shrimp and toss to coat. Add the flour and toss until each shrimp is lightly coated in flour.
Heat the butter and olive oil in a large deep skillet over medium-high heat until hot and shimmering.
Add the shrimp in a single layer and cook about 2 minutes per side, until crisp and opaque. Remove the shrimp to a plate and set aside.
In the same skillet, pour in the chicken broth and heavy cream. Season with salt and pepper and additional Cajun seasoning if desired, then bring to a gentle boil.
Whisk in the grated Parmesan until the sauce is smooth and slightly thickened.
Add the cooked fettuccine and the shrimp back to the skillet and toss to coat in the sauce; use a splash of reserved pasta water if needed to loosen the sauce.
Garnish with chopped parsley and additional Parmesan if desired, then serve immediately.