Uhhh....
There are no 16th century "Burgundians" as a people with a separate language. The Ancient kingdom of Burgundy disappeared forever during the time of the Merovingian Franks.
Medieval people from Burgundy - County, or Duchy of, spoke French (although the Franche Comte is French speaking, the HRE was not based oin language, but who owed fealty to the Emperor).
Burgundians, from the early Middle Ages to the modern era, are culturally, and linguistically FRENCH.
Now, people confuse Valois Burgundy as only consisting of the two Burgundies, when in fact, the most important provinces were in the Low Countries, and most of these spoke Flemish (Dutch), although some spoke French (Hainault - which again, was Imperial - not French, although the people of Hainault spoke French.)
Valois Burgundy consisted of a NUMBER of different Duchies, counties, and lordships, and not all people of Valois Burgundy were "Burgundians", in the sense of being from the two Burgundies - in point of fact, only a fraction of the population were represented by the County and Duchy of Burgundy.
In the 16th century, NEITHER the County, nor the Duchy of Burgundy weere a part of the Burgundian inheritance of Maximillian of Austria, Holy Roman EMperor - both had been invaded, and conquered by Louis XI of France, after the death of Charles the Bold, and from that time to this day are politically French, as well as being linguistically, and culturally French.
I hope this clears up a misconception that is painful to the point of causing me a migraine.