And I suspect that the French will scrabble around trying to get the duchy of Burgundy back in any war to come. So Ernst GETTING it and his heirs KEEPING it would be two different matters.
But I wonder how this "pawning" of French provinces will affect the view of Henri IV TTL. OT1H he's securing Brittany (and he'll probably want to make it that, like with Navarre, the succession can't diverge from the French succession to prevent anything like this happening in future), but OTOH, he's WILLINGLY giving up a province (Burgundy) that the French spilled blood over in Louis XI, François I and Henri II's reign to KEEP.
Well, the French would NEVER be able again to take Burgundy because Burgundy, Netherlands and a couple of generations later Lorraine will be all part of the personal possession of the Holy Roman Emperor AND the usual seat of his heir. Without Hungary and with Burgundy and Netherlands, the Austrian Habsburg will concentrate their energy on Germany (and the Burgundian colonies) and in the end this lands (including Alsace) will be all part of the ATL Imperial Germany, born from the centralization of the Holy Roman Empire with the Austrian Habsburg as hereditary rulers.
ATL Henry IV (who will able to free himself of the Guisa once for all as both their main holdings (Guise and Aumale) will be among the lands given to Ernest) will justify the dolorous cession of Burgundy with the absolute need to prevent and neutralize once for all the eventuality of a foreign or worse Austrian Brittany (something for which Louis XI, Charles VIII, Louis XII, Francois I had all fought hard). Better renouncing to Burgundy and other border lands than seeing Brittany transformed in a new, bigger and much more dangerous Calais (by the way, both Calais and the county of Boulogne will be among the lands lost by Franceas more coast and good ports will be among Ernest’s requests)
French nobility and population will understand that (and in any case Henry IV, whatever thing he does, will end assassinated by someone for some reason)