Kinda late in the Renaissance, but maybe a significantly more successful Reformation, beginning earlier and spreading farther. Perhaps the corruption of Pope Alexander VI (1492-1503) stimulates somebody to pull a 95 Theses-style protest earlier, around 1500. This reformation spreads throughout Northern Germany, France, and England. By the time Charles V comes up for election as Holy Roman Emperor two decades later, the electors are split and he doesn't get the election. He decides to use his Austrian, Spanish, and Neapolitan troops to bring the errant princes of Germany to heel, at which point they form an alliance of religion with France and England and an alliance of convenience with several Northern Italian states. If the Reformation can spread eastward, Poland gets involved, Scandinavia goes Protestant as OTL, and the Ottoman Empire takes advantage of the distraction the Austrians are experiencing to make inroads in Southern Europe.
I really don't see this as particularly plausible, but that's the period I know the most about. Prior to the Reformation, which nicely corresponds with the High Renaissance, you don't have the necessary conditions to split Europe into two heavily armed opposing camps - except for the period of the Schism. That might also offer some possibilities, but I'd have to think on it further.
There's also the overall difficulty of carrying off a continent-spanning war with the finances, the governments, and the logistical apparatus in most of Europe during the period. Sustaining long wars overseas will sap the treasury, and the monarchies of Europe are just now getting to the point where they'll be able to feasibly sustain lengthy campaigns countries away without running the risk of instability at home.