Preheat the oven to 375°F. Boil the lasagna noodles according to package directions, then drain and set aside.
In a large skillet, cook the ground beef over medium heat until browned. Add the diced onion, zucchini, and red bell pepper. Cook for 5 minutes until the vegetables soften.
Stir in 3 cups of marinara sauce and the fresh spinach. Simmer for 3 minutes until the spinach wilts, then remove from heat.
In a 9x13 baking dish, spread a thin layer of the remaining marinara sauce. Place 4 noodles on top. Spread half the ricotta over the noodles, then half the beef and vegetable mixture. Sprinkle with 1 cup mozzarella and 2 tablespoons Parmesan.
Repeat the layers with the remaining noodles, ricotta, beef mixture, and cheeses. Cover with foil and bake for 25 minutes.
While the lasagna bakes, mix the softened butter, minced garlic, and parsley in a small bowl. Slice the French bread, spread the garlic butter on each piece, and wrap loosely in foil.
After 25 minutes, remove the foil from the lasagna. Place the wrapped garlic bread in the oven on a separate rack. Bake both for 10 more minutes until the cheese is bubbly and the bread is warm and crisp.