Peel and cut potatoes into 1cm sticks; soak in cold water for 30 minutes, then drain and pat thoroughly dry to remove surface starch.
Heat vegetable oil to 150C and fry potatoes in batches for 5 minutes until softened but not browned; remove and drain on a wire rack.
Season chicken with salt and pepper; heat olive oil in a large skillet over medium-high heat and sear chicken until golden brown, then remove and set aside.
In the same skillet, sauté onion and bell pepper for 5 minutes until translucent; add garlic and both paprikas and cook for 30 seconds.
Whisk flour into the chicken stock until dissolved, then pour into the skillet and return the chicken; simmer for 15 minutes.
Increase frying oil temperature to 180C and fry the potatoes a second time for 3 to 4 minutes until golden and crispy; drain and salt immediately.
Incorporate the sour cream into the chicken mixture by first tempering it with a small amount of hot sauce, then stirring it into the skillet over low heat.
Serve the creamy paprika chicken immediately alongside the golden fries.