"I learned how to make lasagna this way when I worked in France. What makes it French-style is the use of a bechamel (white sauce) instead of ricotta, and Swiss (traditionally Emmental) cheese. Full of great flavor! I always get compliments."
Bring a large pot of lightly salted water to a boil. Cook lasagna noodles in the boiling water, stirring occasionally until tender yet firm to the bite, about 8 minutes. Drain.
Preheat oven to 350 degrees F (175 degrees C).
Combine ground beef, onion, green bell pepper, and minced garlic in a large skillet over medium heat; cook and stir until beef is no longer pink, 5 to 8 minutes.
Melt butter in a saucepan over medium-low heat. Stir in flour; cook for 1 minute. Pour in milk and heavy cream. Cook, stirring frequently, until sauce thickens, about 5 minutes.
Spread 1/4 of the tomato sauce in the bottom of a 9x13-inch baking dish. Cover with 3 lasagna noodles. Spoon 1/3 of the beef mixture over the noodles. Spread 1/4 of the tomato sauce and 1/3 of the white sauce over the beef mixture. Sprinkle Parmesan cheese, salt, pepper, herbes de Provence, and garlic powder on top. Cover with 1/3 of the Swiss cheese and mozzarella cheese.
Repeat layers twice, starting with noodles and ending with cheeses.
Bake lasagna in the preheated oven until top is deeply browned, 30 to 45 minutes.