Melt butter in small sauce pan over medium heat. Whisk in flour and cook for 1 minute. Whisk in the milk and beer and bring to simmer. Stir in the horseradish and Worcestershire sauce. Cook sauce for 2 - 3 minutes, whisking entire time.

Remove sauce from heat. Add cheese and stir until melted. Serve immediately as a dip for the french fries.