Spread the cornbread and French bread cubes out onto sheet pans. Let them dry out for several hours and up to overnight. You want them to be crisp/stale.
Preheat the oven to 350 degrees F.
Heat a large skillet over medium-high heat. Crumble the sausage into the skillet and brown until cooked through, 4 to 5 minutes. Remove the sausage into a large bowl and drain half the grease. Lower the temperature under the skillet to medium. Melt the butter, then add the celery, rosemary, carrots and onions. Cook until the onions are translucent, about 5 minutes. Add the chicken stock, thyme, sage and turmeric and bring to a boil.
Add the bread to the bowl with the sausage and toss to combine. Gradually ladle the broth mixture into the bread and sausage mixture, tossing lightly as you go, until completely combined. Taste and season with salt. If the mixture needs more moisture, you can add more stock as desired. Stir in the parsley and transfer to a baking dish. Bake until golden on top, 20 to 25 minutes.