Preheat the oven to 375°F. Season the chicken breasts with salt and pepper. In a large skillet, heat olive oil over medium heat. Add the chicken and cook for 6-7 minutes on each side, or until cooked through. Remove from the skillet and let rest for 5 minutes before slicing.
In a large pot of boiling salted water, cook the fettuccine according to package instructions until al dente. Drain and set aside.
In the same skillet used for the chicken, melt the butter over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant. Pour in the heavy cream and bring to a simmer. Stir in the Parmesan cheese and nutmeg (if using), and cook until the sauce thickens slightly, about 3-5 minutes.
Add the cooked fettuccine to the sauce, tossing to coat. Slice the chicken and place it on top of the pasta. Garnish with chopped parsley.
For the garlic bread, slice the French bread in half lengthwise. In a bowl, mix together the softened butter, minced garlic, chopped parsley, and salt. Spread the mixture evenly over the cut sides of the bread. Place on a baking sheet and bake for 10-12 minutes, or until golden and toasted.
Serve the Chicken Alfredo with slices of garlic bread on the side.