Preheat the oven to 350°F and lightly spray a 9x13-inch baking dish with cooking spray.
Cook the spaghetti according to package directions until al dente, then drain well in a colander.
In a large bowl, combine the chopped cooked chicken, both cans of cream of chicken soup, the sour cream, drained spinach, 1 cup of the shredded Monterey Jack cheese, and the minced garlic. Stir until evenly mixed.
Add the cooked, drained spaghetti to the bowl and toss gently to coat the pasta with the sauce and chicken mixture.
Transfer the mixture to the prepared 9x13-inch baking dish and spread into an even layer.
Sprinkle the remaining 1 cup shredded Monterey Jack cheese over the top, then evenly scatter the remaining French fried onions over the cheese.
Bake uncovered for 40 to 50 minutes, until the casserole is heated through and the topping is golden; remove from oven and let rest a few minutes before serving.
