Preheat oven to 300 degrees.
Arrange the French bread and cornbread in a single layer on rimmed baking sheets.
Bake, tossing occasionally, until completely dried out, 35–50 minutes.
Let the bread cool on the baking sheets, then pour into a very large bowl.
Meanwhile, heat a large skillet over medium-high.
Cook the sausage, making sure to break it into crumbles, until just browned, 8–10 minutes.
Transfer to bowl with bread but do not stir.
Heat the stick of butter in the same skillet over medium-high.
Add the onions and celery, and cook stirring often, until just beginning to brown, about 10 minutes.
Add the garlic and cook, stirring constantly, for 1 minute.
Add to bowl with bread mixture and let cool.
Whisk the eggs, chicken broth, parsley, sage, and thyme, in a medium bowl; season with sea salt and freshly cracked pepper, to taste.
Add egg mixture to bread mixture and fold gently until thoroughly combined.
Increase oven temperature to 350 degrees.
Butter a 9 x 11 baking sheet with butter or cooking spray. Transfer stuffing to prepared dish, cover with foil, and bake for 40–45 minutes.
Uncover and continue to bake until set and top is browned and crisped, 45–50 minutes more. Remove from the oven.
Serve and enjoy.