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Using meat pounder, gently pound thickest part of each breast to ¾-inch thickness between 2 pieces of plastic wrap. Sprinkle chicken with 1 teaspoon salt and pepper. Place flour in shallow dish. Working with 1 breast at a time, dredge lightly in flour, shaking off excess; transfer to plate.
Melt 2 tablespoons butter in 12-inch nonstick skillet over medium heat. Add chicken and cook until lightly browned, 4 to 6 minutes per side. Return chicken to plate.
Add shallots, garlic, remaining ¼ teaspoon salt, and remaining 1 tablespoon butter to now-empty skillet and cook until shallots are softened, about 3 minutes. Stir in cream and return chicken to skillet.
Reduce heat to medium-low; cover; and cook until chicken registers 160 degrees, 5 to 8 minutes. Transfer chicken to serving platter. Whisk 2 tablespoons mustard and tarragon into cream sauce, then season with salt, pepper, and remaining mustard to taste. Spoon sauce over chicken. Serve.