As in “The Playford Ball” Triple Minor Longways
Playford's Dancing Master of 1728.
Adapted by Cecil Sharp
Recording: orleans_baffled-068-bn12pb04.mp3.zip
orleans_baffled--010.mp3.zip

A  1-2 1st couple cast down to second place, 
       2nd couple moving up. 
   3-4 1st and 3rd couples poussette half-way 
       clockwise, 1st man pushing. 
   5-6 1st couple cast up to second place, 3rd couple moving down. 
   7-8 1st and 2nd couples poussette half-way clockwise, 
       1st man pulling. 
     9 1st corners change places.
    10 2nd corners change places.
 11-12 1st couple face up, 2nd couple down: circular hey, three changes.

Another rendition.

   A    6  First couple cast to middle, second lead up
        6  First couple half-poussette with third
           (Start by first man and third lady advancing)
   B    6  First couple cast to middle, third lead down
        6  First couple half-poussette with second
           (Start by first lady and second man advancing)
   C    6  In two top couples: first corners cross, second corners cross
        6  Same four do three changes of a circular hey (starting along sides)

Video: https://www.youtube.com/watch?v=kww8BlnAupE

The title perhaps refers to Philippe II (1674-1723), Duke of Orléans, a powerful member of the French royal family.