Cut the French bread in half crosswise. Cut a thin horizontal slice from the top of each portion; set aside. Using a paring knife, carefully remove bread from the center of each portion, leaving a 1/4-inch shell. Reserve the center pieces of bread for another use.
Quarter cherry tomatoes; halve grape tomatoes. In a medium bowl combine the tomatoes, mozzarella cheese, cucumber, onion, mint, vinegar, oil, salt, and white pepper. Line bottoms of bread shells with basil leaves. Fill with tomato mixture. Replace bread tops. Wrap each sandwich in plastic wrap and chill for at least 4 hours or overnight. Makes 2 servings.