NEW ORLEANS—The courtrooms handling illegal immigration cases here are tucked into the fifth floor of a white skyscraper on the bank of the Mississippi River. A few floors below is a Saks Fifth Avenue, reputed to be one of the tony department store’s most profitable locations, and a few floors above is a U.S. passport…

NEW ORLEANS—The courtrooms handling illegal immigration cases here are tucked into the fifth floor of a white skyscraper on the bank of the Mississippi River. A few floors below is a Saks Fifth Avenue, reputed to be one of the tony department store’s most profitable locations, and a few floors above is a U.S. passport…