Presuming the unavailability of Mary Tudor for whatever reason, who could have been the third wife of Louis XII of France?
What are the impacts on France (and Brittany) and the Italian Wars if said wife is pregnant with a son when Louis XII expires as per OTL?
Would Bona Sforza as Queen have added any legitimacy to the French claim on Milan?
Things that will most likely change from OTL:
1- I'm going to guess that Mary died, as her elder sister Elizabeth did, as a child. If that is the case, with no elder Mary to be offered to and then taken away from Charles of Castille, relations with the Hapsburgs go a little better than OTL, as the fallout doesn't leave Charles without a bride. In this case, it means Charles is most likely from the start betrothed to Isabella of Portugal, who is honestly the most obvious choice and one that I don't understand was ignored until the 1520s OTL. With this union more of a certainty, it most likely happens a year or two earlier, possibly giving him different children than OTL. If nothing else, the lack of Mary Tudor the Elder means that the Grey and Clifford heiresses are not an option and thus Margaret Douglas is probably granted her wish and her children go much further up the Henrican succession. And who knows what happens to Charles Brandon ITL? Most likely he remarries some other, more suitable heiress and has a few children. Not really ever rising above maybe an Earldom. Though, judging by his closeness to the King, the Dukedom may have come much later, though probably not.
2- Louis XII, no matter who he marries, probably doesn't die so quickly. He's not going to marry anyone known as the 'Most Fair Princess' as OTL and thus maybe goes on another year. As for who he marries, they are either anti-Hapsburg or at least pro-France. Honestly, as you mentioned Bona Sforza seems a good choice. If they are married in 1515, upon Bona's potential husband Maximilian Sforza's defeat, then Louis would definitely use her claims to control Milan. OTL, with a husband similar age, she managed 6 children, two of which were male. ITL, with a husband who seemed to father more boys than girls (out of 6 children that had on obvious gender, 4 were male) she probably gives Louis the son he wants. If he still dies before 1520, let's say 1518 (which seems fair, with a not so outstandlingly beautiful wife and some time to rest after the death of Anne of Brittany) then Bona most likely gives him 2, maybe 3 children. Let's say 2 boys and a girl, which fits the pattern he shows OTL with the pregnancies OTL: Marie (b.1516), Louis (b.1517) and Charles (b.1518).
3- With Louis with Bona, Sigismund most likely marries some other princess. One that I would seriously consider is either Isabella or Mary of Austria (not Eleanor, Poland is too far to waste your eldest sister on) or even Anna of Oldenburg, who's intelligent religious decisions and many children should guarantee the throne and maybe give Poland a succession crisis if she tries what she did OTL, giving all of her sons a stake in their holdings.