Combine the butter, mayonnaise, green onions, garlic, Parmesan cheese, and Monterey Jack cheese in a large bowl. Cut each half of French bread into 4 pieces. Spread the cheese mixture evenly on the bread pieces.
Bake in the preheated oven for 8 minutes. Set the oven to broil; broil until hot and bubbly, about 2 additional minutes.
