He was assassinated on the eve of preparing to attack and retake Paris. His assassination was quite brutal in the sense that his army essentially melted away and the capital wasn't retaken. The League is still going to remain powerful simply because Henry III was afraid of them, and that he openly accepted the King of Navarre as his heir, despite his Protestantism.
I don't see Henry of Navarre converting because there is no need, Henry III is going to accept him as heir anyways. He only did so under the influence of his Catholic mistress IOTL anyways, and even though he did become Catholic, many believed he was still following the Protestant religion.
Henry III was pretty weak though; he pandered to both the Protestants and the Catholics when possible. He attempted to extend toleration to the Protestants in 1576, but the Duke of Guise forced him to rescind the Edict. And although he did attempt to strip Henry of Navarre of his rights to the throne in 1584, it was not technically legal, as French Salic Law is quite fuzzy and hence why people debate it today in regards as to who the true King of France would be. He quickly joined forces with Henry of Navarre anyways, after he had the Duke of Guise and Cardinal of Guise murdered.
If he survives and takes Paris, we may see the King attempt to negotiate with the Leaguers, although his authority is all but shot. I can see them attempting to force Henry to name the Cardinal of Bourbon as his heir, although he dies in 1590. No doubt, the religious affairs will continue to flare up as long as Henry III lives. He just isn't as decisive as Henry of Navarre. I can't see them actually being able to push through anything and actually enforce it in such a climate.