Philip II of Spain and Elisabeth of Valois have a son

Exactly as it says on the tin, what might the consequences be if Philip II of Spain and his wife Elisabeth of Valois had a son in 1568, and what might've happened had Elisabeth survived the pregnancy?
 
This son, let's call him Philip, might come around 1561/1562, before the stillborn twins in 1564. He would be the brother of Isabella and Catherine and would be of an age with the Austria Princess Margaret of Austria (1567–1633), who might be his Queen. He's lead to a slightly cleaner bloodline and might have more of an affinity for France, though most likely not.
 
If his older half brother Don Carlos lives, Philip II could try to put him on the French or English throne as did with Isabella in OTL.
 
Philip II did not want Don Carlos to rule.

So this Philip born by Elizabeth of France, if he lives long enough, will just become king Philip III in 1598 of OTL Philip III born by Ann of Austria. But this son will anyway be a Habsburg and a spanish ans he will have no legal claim to the throne of France.
 
To be honest I've always wanted to see a TL in which Isabella Clara Eugenia got to rule Spain in her own right (France optional).
 
This son, let's call him Philip, might come around 1561/1562, before the stillborn twins in 1564. He would be the brother of Isabella and Catherine and would be of an age with the Austria Princess Margaret of Austria (1567–1633), who might be his Queen. He's lead to a slightly cleaner bloodline and might have more of an affinity for France, though most likely not.

Interesting, so if this Philip is around thirty years old and married with children of his own when he becomes King, what consequences might this bring?
 
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