Season both sides of the chicken breasts with salt and black pepper.
Heat olive oil in a large skillet over medium heat.
Add the chicken breasts to the skillet and cook for 5-6 minutes on each side until golden brown and cooked through. Remove chicken from the skillet and set aside.
In the same skillet, add the thinly sliced onions and cook over medium heat, stirring occasionally, until caramelized and golden brown, about 15 minutes.
Add the minced garlic, dried thyme, and dried rosemary to the onions and cook for 1 minute until fragrant.
Sprinkle the all-purpose flour over the onions and stir well to combine. Cook for 1-2 minutes to remove the raw flour taste.
Gradually pour in the beef broth while stirring constantly to avoid lumps. Bring the mixture to a simmer and cook until slightly thickened, about 3-4 minutes.
Stir in the heavy cream and continue to simmer for 2 minutes until the sauce is creamy and smooth.
Return the cooked chicken breasts to the skillet, nestling them into the sauce and onions.
Sprinkle the shredded Swiss cheese evenly over the chicken breasts.
Cover the skillet and cook for an additional 3-5 minutes until the cheese is melted and bubbly.
Remove from heat and serve the creamy French onion chicken hot.