Preheat the oven to 350 degrees

Spread the cornbread and French bread cubes on a baking sheet. Bake for 15 minutes, or until dry and slightly toasted.

While the bread is baking, heat the olive oil in a large skillet over medium heat. Add the sausages and cook until browned, breaking them up with a spoon as they cook.

Add the celery, onion, sage, thyme, salt, and pepper to the skillet. Cook until the vegetables are softened, about 5 minutes.

Remove the skillet from the heat and let the sausage mixture cool for 10 minutes.

In a large bowl, combine the cornbread cubes, French bread cubes, sausage mixture, chicken broth, and eggs. Mix well.

Transfer the dressing to a greased 9x13 inch baking dish.

Bake for 25 minutes, or until the dressing is set and the top is golden brown.

Serve immediately.