Your Philip becomes king of Spain as an ATL Philip III.
Your Charles becomes king of France as an ATL Charles X.
Your Antoine becomes king of Navarre as an ATL Antoine I (but not king of France, except if ATL Charles X dies without any son and his uncles still die without any son too).
OTL Henry III stays king of Poland, meaning Stephen Báthory stays prince of Transylvania and Sigismund Vasa stays king of Sweden.
ATL Philip III would be much less inbred than OTL Philip III and may have better intellectual abilities, meaning he may be a better king. Of course, this is pure speculation.
Philip II may or may not marry Anna of Austria after Elisabeth of Valois' death. If he still marries her and still has a surviving son with her, this surviving son is likely to inherit Netherlands but it would be a poisoned gift.
ATL Charles X would still be a very young child at the time of Charles IX's death, meaning there would be a regency. Obviously, Elisabeth of Austria is the logical choice. However, she did not even speak French. I don't know at all what kind of relationship she had with her mother-in-law Catherine de Medici in OTL. Maybe she would agree to let regency to Catherine who is far more experienced.
ATL Antoine I is born in 1573. It means he is born at French court, before the time his father Henry of Navarre escaped (or was let to escape). As a result, he is likely to be raised in French court by his mother and his grandmother and, therefore, would be Catholic.
The years after Charles IX's death are likely to be very difficult with an infant king and a regent either totally unexperienced (if that's Elisabeth) either overall hated (if that's Catherine) to deal with the Malcontents.
However, at least, succession would be secured for Catholics meaning, on the long term, it may avoid the crisis with the League. It is likely that some Leaguers would still have requirements but it would not turn as bad as in OTL.
As for Protestants, they are likely to be defeated sooner or later (especially if the next king of Navarre is Catholic).
Henry of Poland would have to deal with his new kingdom. In OTL, it was pretty difficult for him but we have to take into account that he stayed only four months. He would probably adapt with time. He would have no choice anyway.
An important point is his marriage. If he wants to have a son and wants this son to have a chance to be elected after him, he needs to marry a Jagiellon descendant.
He was supposed to marry Anna Jagiellon in OTL but she was too old to give him children and he dellayed the marriage until Charles IX's death. Then, he came back to France.
If he stays in Poland in this ATL, he needs to take a decision about that. I once suggested that, instead of Anna, he may marry her half-niece Elisabeth-Magdalena of Brandenbourg but I was answered this marriage would not help him in any way (
https://www.alternatehistory.com/fo...lives-till-age-60.507162/page-2#post-21747724).
Stephen Báthory would be fine staying in Transylvania, I guess.
Sigismund Vasa would be in a difficult position. He would be the Catholic king of a Lutheran country.
I see four possibilities:
1. He converts to Lutheranism.
2. He is allowed to stay Catholic but Lutherans still dominate the country.
3. He manages to make Sweden Catholic again (ambitious but who knows?).
4. He ends up being overthrown and his Lutheran uncle Charles becomes king as in OTL.
en.wikipedia.org
