Melt butter in a large skillet.
Add onion and garlic; cover and cook over medium heat 10 minutes, stirring often.
Remove cover and cook an additional 20 minutes, stirring occasionally.
Stir in flour; cook 1 minute, stirring occasionally.
Gradually add broth; cook over medium heat, stirring constantly, until thickened and bubbly.
Stir in catsup, mustard, and horseradish.
Remove from heat; set aside.
Brown sausage in oil in a medium skillet over medium heat; remove from skillet, and drain well.
Stir sausage into mustard sauce.
Split French rolls; spoon sausage mixture over roll bottoms.
Cover with roll tops; cut rolls in half, and serve.