A wonderful primary source has been published online by the library of Dresden — Opus Amplissimum de Arte Athletica v.I & II by Paulus Hector Mair. Although not French, the treatises offer over 1200 pages of brilliantly illustrated European physical combat techniques from the 1550’s.
Mair (1517-1579) was a German civil servant born into a wealthy family. He eventually became the City Treasurer and Quartermaster in Augsburg. Mair was apparently obsessed with fencing and combat since his youth, and witnessed the disappearance of Medieval combat techniques in his lifetime. Given his obsession, he compiled a
…massive fencing compendium titled Opus Amplissimum de Arte Athletica (“The Greatest Work on the Athletic Arts”), and in it he compiled all of the fencing lore that he could access. He retained famed Augsburg painter Jörg Breu the Younger to create the art for the text, and according to Hils Mair also hired two fencing masters to pose for the illustrations. This project was extraordinarily expensive and took at least four years to complete. Ultimately, three copies of the massive fencing manual—six volumes in all—were produced, the first entirely in Early New High German, another entirely in New Latin, and a third including both languages.
–Wiktenauer
Pertinent to our study are the incredible color illustrations created by Jörg Breu the Younger for Mair’s treatises. Several illustrations show 16th Century techniques for baton, including the pronated hand positions that later became integral to Baton Federale.

16th Century baton technique implementing the pronated grip that later became integral to French Baton Federale.
Our French brethren at savate-canne.com have conducted a practical investigation into use of the baton techniques as presented by Mair. You can read the results of their systematic study of Mair, Baton de Mair, here (via Google Translate).
There are two more items that I find of interest about Mair and his magnum opus. Mair covers a vast array of weapon techniques in his voluminous study. The reader will find instruction on everything from the use of two-handed swords to farm implements such as sickles and scythes — reminders of the brutal roots of physical combat that are somewhat cleansed from classical French techniques.

Mair’s treatises cover a wide range of physical combat techniques, ranging from two-handed sword to sickles and scythes.
Lastly, Mair paid for his fencing obsession with his life, although not by the sword. Mair’s Arte Athletica was a major endeavor to create, and very expensive. Although he was born into wealth, Mair apparently lived well beyond his means. In combination with the expense of creating Arte Athletica, Mair resorted to embezzling funds from the Augsburg coffers. He was convicted of embezzlement and sentenced to death by hanging in 1579.
You can find Mair’s Arte Athletica Vol. I here, and Vol. II here. A translated view of savate-canne.com’s exploration of Mair’s techniques can be found here. More information about the life of Paulus Hector Mair can be found at Wiktenauer here.
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