My area is food science, which often takes me into food history as well. Parmentier and some others claim to have been successful in making satisfactory bread from potatoes alone, while still others continued to deny it to be possible to make bread from greater than 1 part potato content to 2 parts wheat. I am curious whether these vastly differing results could be attributed to the significant starch chemistry variation between different potato varieties (this spectrum can be simplified as ranging from waxy to floury). Given this variation, it would be necessary to identify what type of potato may have been used in this time and place in order to attempt to recreate the bread. However, I have not managed to find any significant information on the properties or cultivar name of the specific potato that may have been used.
Hi ! I don't know anything about potato history, but I went through Traité sur la culture et les usages des pommes de terre by Antoine Parmentier. In the book, he describes 12 different varieties of potatoes. Among them, he says that the "grosse blanche tachée de rouge" (fat white stained with red) variety is the best suited for bread making :
"La groſſe-blanche tachée de rouge, par exemple, est celle à laquelle il faut ſpécialement s’attacher pour la nourriture des beſtiaux, la préparation du pain & l’extraction de la farine, parce qu’elle est la plus vigoureuſe, la plus féconde de toutes, qu’elle convient à tous les terrains, et ſemble braver toutes les intempéries."
Translation :
"The fat-white stained with red, for example, is the one to which we must especially attach ourselves for the food of the cattle, the preparation of the bread and the extraction of the flour, because it is the most vigorous, the most fertile of all, that it is suitable for all terrains, and seems to brave all the bad weather."
He also says that this variety is the most used in France and the Netherlands. Here is his description of the variety :
"It has dark green leaves, smoother & rougher underneath; the leaflets are broad, oblong, flattened, and pointed; its stems are strong and creeping; its flowers begin to be red, variegated, and end with the gray-of-linen; they are abundant, as well as berries. This variety is the most vigorous, the most fruitful & the most common in our markets; It succeeds in all terrains, but those which are sandy give it an excellent quality: its tubercles are conglomerated and marked internally by red points more or less sensitive. In some cantons where cattle are fed, it is called because of this, a cow's potato: in Flanders it is called savage, and rustic elsewhere. Other species are not known in many provinces; its benefits are invaluable."
I hope this description can help you narrow your search for the variety.
r/botany may also be able to help with this, as they sometimes have discussions about historical varieties of plants