Cook the fettuccine according to package instructions until al dente. Drain and set aside.
In a large skillet, heat the olive oil over medium-high heat. Add the sliced chicken, salt, black pepper, paprika, and cayenne pepper. Cook until the chicken is browned and cooked through, about 5-7 minutes.
Add the minced garlic to the skillet and sauté for an additional 1-2 minutes until fragrant.
Reduce the heat to medium and pour in the heavy cream, stirring to combine. Allow the mixture to simmer for 2-3 minutes until slightly thickened.
Stir in the pepper jack cheese and Parmesan cheese, mixing until melted and smooth.
Add the cooked fettuccine to the skillet, tossing to coat the pasta in the creamy sauce.
Remove from heat and stir in the chopped cilantro and lime juice.
Serve immediately, garnished with additional cilantro if desired.