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updated by @marie-josephine-de-fiennes: 06 Oct 2016 06:06:00AM
Her history is very interesting. She was a cousin of the ill-fated Marie Louis Savoy princesse de Lamballe. Of course as with most movies her role in Marie Antoinette is completely false. I believe in the movie she actually had a baby? Unfortunately she never had children.
Mob Cap that is the term I was looking for. Thank you!
I found this source which I think you will all enjoy. ;D
http://marie-antoinettequeenoffrance.blogspot.com/2010/01/fashion-du-jour-mob-cap.html