In a medium saucepan, melt 2 tbsp. butter over medium heat. Add the pasta; cook until golden, about 2 minutes. Stir in the rice; season. Stir in 2 1/4 cups stock, cover, lower the heat and simmer until tender, about 18 minutes. Fluff with a fork.
Meanwhile, in a small saucepan, bring an inch or two of water to a boil. Add the haricots verts and cook until crisp-tender, 2 to 3 minutes. Drain and let cool.
In a large skillet, heat 2 tbsp. EVOO over medium-high heat. Season the chicken with salt and pepper, add to the pan and cook, turning once, until golden, about 12 minutes. Transfer to a platter and keep warm.
To the same skillet, add the remaining 1 tbsp. EVOO and butter. Cook over medium-high heat until foaming, then add the shallots and garlic; season with salt and pepper. Cook, stirring, for 2 minutes. Stir in the wine and cook for 2 minutes. Stir in the remaining 3/4 cup stock, the creme fraiche, tarragon and mustard.
Slice the chicken and add to the sauce in the pan. Stir in the green beans. Serve with the pilaf.