Preheat the oven to 350 degrees F (175 degrees C). Line a rimmed baking sheet with foil.
Combine ground chicken, bread crumbs, 4 tablespoons French onion soup mix, and pepper in a bowl; blend well. Cover and let mixture rest for 10 minutes.
Portion chicken mixture into balls using a 1 1/2-tablespoon scoop. Press a mozzarella ball into each chicken ball and roll between your hands to enclose the cheese. Place stuffed chicken balls onto the baking sheet.
Bake in the preheated oven until meatballs are lightly browned and cooked through, about 18 minutes.
Meanwhile, heat remaining French onion mix, water, and cream in a saucepan over medium-high heat. Cook until slightly thickened. Serve sauce over stuffed chicken balls.