Cut baguette into 3 even sections. Using a long knife, hollow out the inside of the baguette, removing the bread from inside but being sure to leave some bread along the edges. Set aside.
In a large skillet set over medium heat, heat olive oil. Add garlic, artichoke hearts and spinach. Heat, stirring often until spinach has wilted. Add cream cheese and mozzarella cheese. Stir and allow the cheese to melt, stirring constantly. Once completely melted, remove from heat.
Using a small spoon, fill each piece of hollow baguette with the artichoke cheese mixture. Line the filled bread pieces on a cutting board and gently cut into 1-inch pieces. Carefully keeping the baguette together, transfer the sliced baguette to a large long piece of foil and wrap.
Place the baguette onto a baking sheet and bake in preheated oven for 20 minutes. Remove from oven and serve warm.