Preheat oven to 425 degrees F. Spray a large baking sheet with nonstick spray and set aside.
Carefully cut turnips and potato into French-fry-shaped spears using a crinkle cutter if you have one. Place them in a single layer on the baking sheet and sprinkle evenly with salt and pepper. If needed, use another baking sheet sprayed with nonstick spray.
Bake in the oven until tender on the inside and crispy on the outside, about 30 minutes, carefully flipping spears about halfway through. (The thicker the spears, the longer the bake time.)
In a small nonstick pot on the stove, heat gravy over a low temperature until hot, 1 to 2 minutes.
Once cool enough to handle, transfer fries to a microwave-safe plate. Evenly top with strips of cheese. Microwave just until cheese has melted, about 30 seconds. Garnish with chives, if you like, and set aside.
Give gravy a stir and serve alongside cheese fries. Enjoy!