We've had threads on Henri III not being killed, but what about the Duke of Guise?
This could be interesting fro the French Wars of Religion/French Civil War. If Henri III does take Paris anyway, as noted in a couple other threads, Henri IV may not feel the need to converted to Catholicism and perhaps won't even meet his mistress. I'm not sure how long henri III would have lived, but he'd surely outlive the Cardinal Bourbon, Charles - meaning Henri of Guise might either call on Isabella as an heir from Spain or maybe try to make himself heir? Either way, we could see Henri in control of Paris but with the Catholic League still strong.
OTOH, Henri III could still be assassinated anyway. Moderate Catholics were willing to support henri IV even in OTL, but if this happens, without any outrage over Guise's assassination, suddenly you might get more Catholics turned against the Guises and the League in general; after all, they would have committed regicide with Henri III being int he clear. Charles, the cardinal, may be placed on the throne but there could be a lot more opposition.