Marriage Between Jeanne III of Navarre and Sigismund II Augustus?

There's been quite a few threads on potential alternate brides for Sigismund II Augustus, but I haven't been able to find any proposals for this specific alternate marriage.

So let's say that, for whatever reason, the marriage arrangement between Jeanne d'Albret and Antoine de Bourbon falls apart (or is never proposed) and she is never married to him, while Sigismund II Augustus does not marry Barbara Radziwill. Could a marriage between Jeanne III and Sigismund II take place instead? Would it be something that the French crown tries to propose? It could bring Poland into an anti-Hapsburg alliance, as a royal (albeit of a miniscule kingdom) Jeanne would be much more acceptable to the Polish nobility and Sigismund's own family than a commoner mistress like he married IOTL.

Potential downsides, of course, are that France would be giving up on the opportunity to fully place Navarre under their control for another generation at least, the distance between France and Poland means that a marriage alliance may not be that useful to either side, and there is the absolute wildcard of Jeanne III's preferences and feisty personality-though I can see her striking up a correspondence with Sigismund II, resulting in both at least coming into the marriage intrigued and attracted to each other.
 
Why Jeanne, when Marguerite was not married yet? And besides her there was also another relative of French king available-Anna d'Este, whom Bona wanted to see as daughter-in-law.
 
as a royal (albeit of a miniscule kingdom) Jeanne would be much more acceptable to the Polish nobility and Sigismund's own family than a commoner mistress like he married IOTL.

Barbara Radziwiłł wasn't a commoner, she was daughter of one of most proficient Lithuanian houses, she hailed from top aristocracy. She was perceived in Poland as foreign, yes, but so would be Jeanne.
And middle nobility would look for excuses to limit the king's power anyway.
 
Barbara Radziwiłł wasn't a commoner, she was daughter of one of most proficient Lithuanian houses, she hailed from top aristocracy. She was perceived in Poland as foreign, yes, but so would be Jeanne.
And middle nobility would look for excuses to limit the king's power anyway.
She wasnt from a sovereign or formerly sovereign house, and a subject of Sigismund to that.
 
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