I also asked that some days ago, but didn't have many replies:
https://www.alternatehistory.com/discussion/showthread.php?t=124253
The first thing I can think is that legally the new king is the 06 years old Prince of Condé, Henry II, who however was regarded as a bastard by Henry IV and the court. Also, you would have the division of France and Navarre once more, as the prince of Condé didn't have rights to the Navarrese throne. The new monarch of Navarre is the Protestant Catherine, sister of Henry IV. If she dies childless than the throne goes to the Rohan family, who also were Protestants. We might see Navarre remaining as a small, independent and Protestant kingdom in Southern France.