Henri probably could have won without converting, but would never have been as secure, and there would have been still more bloodshed, which his conversion averted. A section of Catholics would never have accepted a Protestant as King of France, whereas the Protestants didn't really have anyone else to turn to so, though no doubt feeling betrayed, would continue to support him. So in that sense converting was a win-win for Henri.
The Infanta Isabella Clara Eugenia, who by the way was Henri II's granddaughter, Henri III's niece, was actually declared Queen Regnant of France by the Paris Parlement. She was also mooted at one time by her father as Queen of England, before eventually ending up ruling the Netherlands with her husband. A remarkable woman, England already had one of its own thanks but France could have done worse.