A while back, when I added all of the MFA's Gallerie des Modes plates (minus the ones that are quartered to show four hairstyles) to my fashion history Pinterest boards, I made some non-decade boards where I could group 18th century extant garments, plates, etc. by type. One group was just "misc", as I had only one image described with a particular term. One of these was the robe à la piémontaise.
Every page that I can find that mentions this type of dress is in agreement that the piémontaise was (to be brief) a française with detached pleats. But I'm not really sure where that comes from. The most recent scholarly reference I can find is in Dress in France in the Eighteenth Century, but I am unable to read the citation as the Google Books preview cuts out all but one page of the endnotes. (If anyone could tell me what is cited there, I would be very pleased.) Prior to that - going back in time chronologically - is Dress in Ireland, by Mairead Dunlevy; I can't actually see the whole sentence, but the piémontaise is listed with the française and the anglaise as "versions of early eighteenth-century silk sack-back robes," which makes me not think much of it as a source - the anglaise is not related to the française, and why list the piémontaise there as though it were as prominent? 20,000 Years of Fashion gives the standard definition of independent back pleats. Then there is Marybelle Bigelow's Fashion in History, but I pointed out a few myths about Greek dress in her work in my symposium paper, so I can't take her word for it. And that is as far back as it seems to go. (As far as I can tell on Google Books, anyway.)
I'm certainly not trying to point fingers at people for going along with what established scholars have said, and I'm not trying to say that this plate is necessarily correct, that the piémontaise was definitely a gown with a back cut like a française and a skirt cut like a polonaise. But this is the only image I've seen that has a picture and labels it "piémontaise", and I can't find any contemporary written descriptions of it. So where did the standard definition come from, and why is it so dominant?
Addendum: I linked to La Couture Parisienne as an example of the "detached pleats" definition of the piémontaise; however, the gown pictured does also fit with the fashion plate's definition in that the skirt seems to have rounded front corners and is trimmed all the way around, and is draped up.
Edited to add: It is rather embarrassing, but I must admit that I am entirely incorrect on this matter. The fashion plate and description is far from being posted as of this moment (book 13, plate 6) but it is quite explicit that the piémontaise has detached pleats which are fastened to the collar of the gown. Still, now we have a primary source to cite in support of the definition, rather than a loop of secondary and tertiary ones!