In a large pot, simmer the whole chicken with the carrot and celery in enough water to cover until the chicken is cooked through, about 1 1/2 to 2 hours.

Once cooked, remove the chicken from the pot and allow it to cool.

Remove the carrot and celery as well.

Refrigerate the chicken and broth separately overnight.

The next day, skim off any fat that has solidified on top of the broth.

Discard the fat along with the carrots and celery.

In a saucepan, combine the French onion soup with the chicken broth and bring it to a boil.

In a separate small bowl, mix flour with water to create a thickening paste.

Gradually whisk the flour-water paste into the boiling broth until the desired thickness is achieved.

Strain the gravy to remove any remaining onion pieces.

Preheat the oven to 400°F (200°C).

Roll out half of the pie crust and line the bottom of a 9-inch pie dish with it.

Remove the chicken meat from the bones and cut it into bite-sized pieces.

Place the chicken pieces in the bottom crust.

Pour the prepared gravy over the chicken in the pie dish.

Roll out the remaining pie crust and place it over the top of the pie.

Crimp the edges to seal, and make several slits in the top crust to allow steam to escape.

Bake in the preheated oven for about 30 minutes, or until the crust is golden brown and the filling is bubbling.

Let it cool for a few minutes before slicing and serving.