Thanks all!! After researching all the options and studying what I have, I think batiste is the closest. It definitely brings to mind Christening gowns and historical re-enactment undergarments.
Cotton Batiste is a semi-sheer, lightweight fabric with a soft face and a slight crispness. Highly used for Christening gowns, for nightgowns, as an underlining for Wedding gowns, and in historical reenactment garments such as chemises and underpinnings
https://www.voguefabricsstore.com/cotton-batiste-128-60-white.html?xid=qngP4RbjoIjMaHryk02z2IoK1HvxdKFX