@Prince di Corsica a reasonably common, but still nice take on the dual monarchy,
How were you intending for Edward of Woodstock to survive Shrewsbury (if indeed Henrí III de France/Henry VII of England is Edward's son ITTL).
Are you feeling that in this time line, that it would become a triple bloc. monarchy (of those shown here) of England, France and Burgundy, or would Burgundy get split off to another son e.g.?
Henry VII/III is the son of Charles the Bold and an alt-daughter of OTL Henry VI. He inherits the kingdoms directly from his maternal grandfather.
The plan is for a triple bloc, since it is compact enough territotially to keep together.