Well, his son is obviously heir to the throne but by the time when HIII is assassinated he is still a child and a Royal Party is most probably weaker than the Catholic League (financed and backed by Spain) and the Protestants led by Henry of Navarre. With Catherine Medici already dead, the Royal Party does not have an obvious leader capable of making the political decisions so a lot depends on who takes control of the young king. As his uncle and the 1st Prince of Blood, Henry of Navarre should be a regent but this causes the obvious problems. If he ends up in the hands of the Catholic League then the Duke of Mayennene supports him as a Catholic king instead of Cardinal de Bourbon and the war is going on. Now, in OTL Henry was regularly beating his opponents and kept Paris under close blockade until it was relieved by Alexander Parma. This hardly changes but Phillip II May decide to marry the young king to the infanta (in OTL he pushed her candidacy to the French throne but was rejected by Mayenne & Co). This may mean a greater Spanish involvement but, realistically, Phillip did not have enough troops to subdue the Dutch and could spare Parma for only a limited time so I would not push this option too far. Anyway, none of the sides is strong enough to gain a de isive victory so, sooner or later, some compromise should be achieved (in OTL Mayenne executed most of the radical leaders of the Catholic League so the common sense could prevail).
Specific form of the compromise is anybody’s guess so we can assume somewhat modified version of the Ecict of Nantes. But as soon as the peace is signed, Henry has a legal right to require the regent’s position (and the armed force to back up his claim). From this point onward the things are completely unpredictable ( Spanish marriage or its absence would be only one of the numerous factors).