Heat a large frying over medium-high heat. Drizzle in the vegetable oil and add the beef chuck. Cook until the beef is browned.
Gradually whisk in the beef broth until the mixture is smooth. Bring to a gentle simmer and cook for 15 to 20 minutes, stirring occasionally, until the gravy thickens to your desired consistency.
Preheat your oven to 450°F. Arrange the French fries on a baking sheet and bake until crispy and golden, about 12 to 17 minutes.