When it comes to corporate colors, brown belongs to United Parcel Service Inc., Owens Corning protects its own shade of pink, and Tiffany & Co. has domain over robin's-egg blue.

On Tuesday, the famed French shoemaker Christian Louboutin SA stepped into the U.S. 2nd Circuit Court of Appeals in Manhattan to make the case that it should effectively own the exclusive right to use red—it calls the shade "China Red"—to coat the bottoms of its popular, pricey high-heeled shoes.

In front of a large and conspicuously well-dressed audience—more than a few women present wore red-soled shoes— lawyers for both sides made their arguments.

"Christian Louboutin has created one of the more iconic trademarks of the 21st century," argued attorney Harley Lewin, before a three-judge panel. "Louboutin turned a pedestrian item into a thing of beauty."

Mr. Lewin and his client were in court hoping to reverse a lower-court ruling that appeared to suggest Louboutin shouldn't be allowed to hold a trademark for its signature red-soled shoes, sported in recent years by red-carpet A-list celebrities nationwide, from actresses Scarlett Johansson and Halle Berry to singers Beyoncé and Christina Aguilera.