What if Charles III, Duke of Bourbon Survives (in 1527) and Has a Surviving Son?

What if this guy:

https://en.wikipedia.org/wiki/Charles_III,_Duke_of_Bourbon

--would have survived (in 1527), spent the rest of his life somewhere outside of France, and had a surviving (Catholic) son sometime before his death (say, sometime in the 1550s, when he would have been in his 60s). Let's say that the House of Valois still becomes extinct in the 1580s or 1590s in this scenario. Thus, what exactly would occur afterwards? After all, this (Catholic) son of the Duke of Bourbon would have had the strongest genealogical claim to the French throne, but his father previously committed treason against France and spent the rest of his life in exile. Meanwhile, the House of Bourbon-Vendome had no traitors against France in their family but also had the issue of many of their members being Protestants.

Anyway, how exactly do you think that this succession dispute in France would have been resolved in this scenario?

Any thoughts on this?

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Also, to clarify, here is what exactly the succession dispute is going to look like in this scenario:

Louis I, Duke of Bourbon (grandson of French King Louis IX) -> Peter I, Duke of Bourbon (eldest son of Louis I, Duke of Bourbon) -> Louis II, Duke of Bourbon -> John I, Duke of Bourbon -> Louis I, Count of Montpensier -> Gilbert, Count of Montpensier -> Charles III, Duke of Bourbon (committed treason against France and died in exile in this scenario) -> Charles of Bourbon (the (Catholic) surviving son of Charles III, Duke of Bourbon in this scenario).

Versus:

Louis I, Duke of Bourbon (grandson of French King Louis IX) -> James I of Bourbon, Count of La Marche (youngest son of Louis I, Duke of Bourbon) -> John of Bourbon, Count of La Marche -> Louis of Bourbon, Count of Vendome -> John of Bourbon, Count of Vendome -> Francis of Bourbon, Count of Vendome -> Charles of Bourbon, Duke of Vendome -> Antoine of Bourbon, King of Navarre -> Henry III of Bourbon, King of Navarre.

Pretty complicated, eh? ;)
 
Also, TL;DR version: One claimant has a stronger claim to the French throne for genealogical reasons but has a shadow cast upon his claim due to his father committing treason and dying in exile (and with him himself being born in exile). Meanwhile, another claimant has a weaker claim to the French throne for genealogical reasons but has an advantage in the fact that none of his ancestors have ever committed treason against France. Also, the first claimant here is Catholic while the second claimant here is Protestant (but can convert to Catholicism if necessary).
 
Is my question here sufficiently clear for everyone?

Oh, and to clarify--I think that the Catholic League might support the son of Charles III, Duke of Bourbon in the French succession dispute in this scenario.
 
The marriage between Eleanor of Austria and Charles III needs to happen, in that case Bloody Mary would be the one that marries Francis I.
 
The question of why Karl would marry Eleanor off to the Constable is on the table? Karl might've offered the marriage, but I truly think that a Spanish infanta/Austrian archduchess/Burgundian princess can do slightly better than a landless cadet (since that's what Bourbon was after he was declared a traitor, his lands went to the king's mother). It to my mind proves that the Habsburgs have a long tradition of promising the sun, moon and stars to get what they want.
 
The question of why Karl would marry Eleanor off to the Constable is on the table? Karl might've offered the marriage, but I truly think that a Spanish infanta/Austrian archduchess/Burgundian princess can do slightly better than a landless cadet (since that's what Bourbon was after he was declared a traitor, his lands went to the king's mother). It to my mind proves that the Habsburgs have a long tradition of promising the sun, moon and stars to get what they want.

That was not the whole story, duke Charles III of Bourbon had a very bad relationship with king Francis I of France, well before he offered his services to Charles V.
Francis had stripped him from the governship of Milan; he was denied a commandment during the French campaigns in the Low Countries; and finally the king's mother claimed the estates, which had belonged to the wife of Charles III, Suzanne of Bourbon (from the elder Bourbon branch, Charles was from the Bourbon-Montpensier branch) and Francis ended up confiscating a part of Bourbon lands on his mother's behalf, before a lawsuit was opened.

In other words Charles III had good reasons to dislike Francis, but Charles V never gave as much as he had promised either, OTOH he had switched sides in 1523 and IOTL died in 1527.

Also Charles/Karel V would deem Charles III to be too low born for his eldest sister Eleanor.
 
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