Prehaps a more interesting POD surrounding Bartholomew's Day Massacre, would be that Francis Walsingham (Elizabeth I's ambassador/Spymaster in France) died doing it. Whether he's actually killed by the mob or he is assassinated or the undefined illness that he got in 1570, and suffered from to his death, is the actual culprit is not important, mainly as noone would believe it not being foul play, specially if it also involved Henry of Navarre dying as OP suggested.
Suddenly we would have a very unamused English Queen (and to a lesser degree every other non-catholic Christian Rulers and prehaps even a couple of Catholic Rulers), ready to throw everything (and the mandatory kitchen sink) at stopping the religiously motivated killings, and if some Catholics die, then so be it.