Preheat the oven to 350°F (175°C) and lightly spray a 9x13-inch baking dish with cooking spray.
Bring a large pot of salted water to a boil and cook the 12 oz dried spaghetti according to package directions until al dente; drain well.
In a large bowl, combine 4 cups chopped cooked chicken, the two 10.5-oz cans of unsalted cream of chicken soup, 16 oz sour cream, the drained 10 oz package of spinach, 1 cup shredded Monterey Jack cheese, and 2 minced garlic cloves; stir until smooth and evenly mixed.
Add the cooked and drained spaghetti to the bowl and toss gently until the pasta is fully coated with the chicken mixture.
Pour the pasta mixture into the prepared 9x13-inch baking dish, spreading it into an even layer.
Top with the remaining 1 cup shredded Monterey Jack cheese and sprinkle the remaining French's French fried onions over the cheese.
Bake uncovered in the preheated oven for 40 to 50 minutes, until the casserole is hot and bubbly and the top is lightly browned; remove and let rest a few minutes before serving.