I guess it would also depend on what the duke of Burgundy's relationship with his son/half-brother-in-law is like, I suppose. Charles might treat Carlos similarly to how he treated Edward IV - he only supported him when it was in his (Burgundy)'s interests to do so, and wanted his help taking on France, but then didn't actually want him (Edward) in any territory controlled by Burgundy IIRC. So Edward flipped him the bird and the result was the Treaty of Picquigny.
Besides, wasn't Carlos (or Juan II) ICR which, extremely pro-French while the other was anti-French?
Well the instincts of Karel de Stoute (Charles the Bold, literally, which is probably best translated from Dutch to French as Charles le Hardi, not Charles le Téméraire, which fits the narrative of Royal French adversaries better) weren't that bad there, since that was the basic idea; however he utterly lacked the diplomatic finesse to accomplish this. For all his ambitions he never could live up to his father Philippe le Bon/Filips de Goede.