Simmer the vegetables in the broth for 5 minutes. Drain and set aside the vegetables and broth. In the same pot, melt the butter. Add the flour and cook for 1 minute, stirring with a whisk. Add the broth, milk, and wine. Bring to a boil, stirring constantly. Reduce the heat, simmer for 2 minutes, stirring. Add the chicken, vegetables, tarragon, salt, and pepper. Let cool. Prepare the pie and bake in the oven at 425 F for the first 10 minutes, reduce the heat to 350 F and bake for 35 minutes, until the pastry is golden brown.