Place a baking sheet on the middle rack of the oven, and preheat to 450 degrees F.
For the aioli: In a small bowl, stir together the mayonnaise, mustard, garlic and a generous grinding of black pepper. Refrigerate while you make the fries.
For the fries: In a large bowl, toss the carrots, russet potatoes and sweet potatoes with the olive oil, granulated garlic, 1 teaspoon salt and several grinds of black pepper. Divide between the preheated baking sheets. Bake until crisp and golden, rotating the baking sheets from top to bottom and tossing the fries once halfway through, 18 to 20 minutes.
Transfer the fries to a serving plate and serve with the aioli.