Preheat the oven to 350°F (175°C).
In a mixing bowl, combine the sour cream, mayonnaise, softened cream cheese, 1 cup Parmesan, and minced garlic; beat or stir until smooth and evenly blended.
Fold the drained, chopped artichoke hearts and the thawed, well-drained spinach into the cheese mixture until evenly distributed.
Slice the French bread loaf lengthwise or into thick slices and arrange cut side up on a parchment-lined baking sheet.
Spread the spinach-artichoke mixture evenly over the bread, then sprinkle the mozzarella on top.
Bake for 10 minutes, then switch the oven to broil and broil for about 1 minute until the cheese is bubbly and lightly browned—watch closely to avoid burning.
Remove from the oven, let cool briefly, slice if needed, and serve warm.