For the fries: Prepare the French fries according to the package instructions.
For the country ham gravy: Place a large saute pan over medium-high heat. Add the butter and ham. Cook, stirring frequently until the ham is crispy and the butter just starts to brown, 6 to 8 minutes. Use a slotted spoon to remove the ham to a paper towel-lined plate.
Add the flour to the pan and whisk to form a smooth paste. Continue to whisk while pouring in the stock. Bring to a simmer and cook until thick enough to coat the back of a spoon, about 5 minutes. Whisk in the mustard, lemon juice and black pepper. Set aside in a warm area, until ready to serve.
For the white cheese sauce: Pour the milk into a small saucepot over medium heat and bring to a simmer. Add the Cheddar, mozzarella and cornstarch and whisk until the cheese melts and a thick sauce is formed, about 3 minutes. The sauce will thicken more as it cools.
Spread the fries onto a large serving platter. Generously pour the gravy and cheese sauce over the fries. Sprinkle with the crispy country ham bits and green onion. Serve with lots of napkins.