Season chicken with salt.

Heat butter in a skillet over medium-high heat. Cook chicken until outside firms up and inside is still medium-rare, 2 to 3 minutes per side. Transfer chicken to a plate and let cool.

Reduce heat to medium. Combine green onions, red bell pepper, and jalapeno in the skillet. Add a pinch of salt. Cook and stir until softened, about 5 minutes. Increase heat to high. Pour in chicken broth. Stir until liquid is mostly evaporated. Stir in cream. Bring to a boil, reduce heat, and cook until sauce is reduced to desired thickness, 6 to 10 minutes.

Cut chicken into evenly sized cubes. Add chicken, accumulated juices, and creme fraiche to the sauce. Cook until chicken is no longer pink in the center, 3 to 7 minutes more. Season with salt, pepper, and cayenne. Turn off heat. Stir in tarragon and spoon chicken and sauce over toast.