Menard's double takeout in the 10th end Friday rendered Koe's final stone meaningless, giving Quebec a 7-5 win that raised its record to 7-4.
That's one win better than New Brunswick, Newfoundland and Labrador, and Saskatachewan, the three teams tied for fifth spot.
Menard needed the win over Alberta and some help to claim the final playoff spot. Quebec clinched sole possession of fourth thanks to James Grattan of New Brunswick beating Saskatchewan's Steve Laycock in the final round-robin draw.
Despite leading by a point and holding the hammer, Laycock gave up a steal of three to hand Grattan a 9-7 win.
B.C.'s John Morris will face Koe in the 1 vs. 2 Page playoff on Friday night at 9:30 p.m. ET, while Manitoba's Jeff Stoughton takes on Menard in the 3 vs. 4 game on Saturday at 4:30 p.m.