Preheat the oven to 225°C (437°F). Place the french fries on a baking sheet and bake on the middle rack for 15 minutes.
Heat a non-stick pan over high heat and fry the gyros meat for 2 minutes. Reduce to medium heat and continue frying for 3-5 minutes until heated through and lightly browned. (Ready-made gyros are pre-oiled, so no additional oil is needed.)
Add the garlic clove, metaxa, and tomato paste to the pan and stir well. Bring to a boil for 1-2 minutes, then turn off the heat. Stir in the crème fraîche.
Transfer the gyros mixture to a baking dish and sprinkle the grated cheese evenly over the top. Place the baking dish and the baking sheet with fries in the oven and bake for 10 minutes at 225°C (437°F).