I understand that the Royale had two speeds for reverse; does anyone know why...?

 

No that is a question I would love to know the answer to as well!

 

As far as I know, it doesn't have 2 reverse gears. Also asked a friend who said he'd never heard such a thing ... and he would know!

Are you sure you're not mistaken with the train engines? The Royale's engine was so massive (and Bugatti needed the money so bad) it was also used in trains, specifically the "Wagon Rapide" (Fast Railcar). It reached outrageous speeds for the time (170km/h to 190km/h, depending on sources) and looked crazy futuristic!

(however brief searches report it does not have 2 reverse gears)

 

this source says it had total of 2 gears + reverse engaged by separate lever