Well, the Direct Capetians die out AIOTL. Let's say the Bourbon rulers are killed during the War of the League of Cambrai.... and the House of Bourbon dies out due to the lack of a male heir. The Valois dynasty dies out some time in the 1500s or 1600s.
Alright then. So, assuming that the Valois die out at the same time they do in OT, with Henry III (who, regardless as to whether or not he is assassinated, will most likely be dead by 1600), I think the most probably candidate for succession would be one of the legitimated royal bastards. As in France there was no precedent for female succession, the idea would be hotly contested. A legitimated prince would most likely have a better claim anyway, as French private law essentially banned persons from inheriting French property if they were not nationals. Even Charles IX's brother, when elected king of Poland, had to secure letters patent making special exception for him to keep his French lands and titles, as well as his issue's rights of succession. Charles de Valois (b. 1573), duc d'Angouleme and legitimized son of Charles IX by his mistress Marie Touchet would be the most likely candidate.
Another possible route would be the accession of the house of Guise. The Guise family were considered foreign princes, being a cadet branch of the house of Lorraine, and thus of blood royal themselves. Indeed, the house of Lorraine had many historic ties to France, and Louis XIV would later recognize that family as being in line for the throne of France should the "august house of Bourbon" go extinct (in the treaty of Montmartre). While this was over a half a century after this date, it still says something about the historic connections between the house of Lorraine and France. Besides, given the immense power that the Guises had at this time, it would not be surprising if, after the Estates were convoked to grant their approval (as they alone were recognized by many legalists as having the power to change something so fundamental as the succession to the French crown), and Parlement registered an edict to its effect, that King Henry III would vest the succession in Duke Charles of Guise and his male issue.
Most likely, whatever the decision, you'd be looking at a European war, as Philip II of Spain would be apt to press the claims of his daughters by Elisabeth of Valois (sister to King Henry III)