An Independent (and Habsburg) Burgundy

Mary the Rich, Duchess of Burgundy had two sons (Philip the Fair, and a boy named Franz (who died young)) and a daughter, Margarethe (bride-queen of France, princess of the Asturias, duchess of Savoy) before she herself died because she fell from a horse.

What would've happened if Franz had survived and produced children? Would Burgundy be retained as a separate entity from the Holy Roman Empire? Or would he just be a minor Habsburg archduke fobbed off with Tyrol or some other hereditary possession (not Burgundy)?
 
He'd probably receive some assortment of fiefs, Brabant maybe, Tyrol otherwise, but always in submission to his father and brother.

He'd be a safe choice for Duke of Milan at some point: instead of offering the Duchy to Henry FitzRoy or Henry VIII, Maximilian might attempt to marry Francis to Mary Tudor and set the two up in Milan. Alternatively he might get Austria while Philip the Handsome is left all of the Burgundian inheritance and the crown of Castille.
 
When did Max offer the duchy of Milan to either Henry VIII or Fitzroy? It's the first I've heard of it. I know Ludovico Sforza tried to get one of his sons married to Mary Tudor, but this is the first I've ever heard of a Tudor Milan
 
If Franz had survived childhood and produced children, his brother Philip would have still kept the Burgundian inheritance for himself. Maximilian I probably would have made sure Franz inherited the Habsburg hereditary possessions in TTL. The Burgundian inheritance was a combination of Imperial and French fiefs so the survival of Franz would not change that fact. Assuming Philip still marries Joanna of Castile in TTL, one of her older siblings(or their descendants) might live long enough to rule both Aragon and Castile and in that case Philip (and his descendants) could rule an independent Burgundy for centuries.
 
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