Creating Rich and Creamy French Chicken Tarragon is straightforward. Follow these steps for a delightful meal:

1. Prepare the Chicken: Season the chicken breasts with salt and pepper on both sides.
2. Heat Oil: In a large skillet, heat the olive oil over medium-high heat.
3. Cook Chicken: Add the chicken breasts to the skillet and cook for about 6-7 minutes per side, or until golden brown and cooked through. Remove the chicken from the skillet and set aside.
4. Sauté Aromatics: In the same skillet, add the chopped onion and garlic. Cook until the onion is translucent, about 3-4 minutes.
5. Add Liquids: Pour in the chicken broth and bring to a simmer, scraping the bottom of the skillet to deglaze it.
6. Stir in Cream and Herbs: Reduce the heat to low, then stir in the heavy cream, chopped tarragon, and Dijon mustard. Allow the sauce to simmer for 5 minutes until slightly thickened.
7. Combine and Serve: Return the chicken to the skillet, coating it in the creamy sauce. Heat for an additional 2-3 minutes. Serve warm, garnished with fresh tarragon sprigs.