Conor Trainor and Justin Douglas scored tries to help the Canadian men open with a 14-12 win over Scotland before losing 26-7 to Fiji and 24-21 to France and finishing third in Pool C.
Douglas scored against Fiji as the Canadians were tied 7-7 at the half before giving up 19 straight points. The second half letdown was even worse against France with Canada leading 21-0 at the break on the strength of tries by Douglas, Lucas Hammond and Sean Duke.
France scored four tries in the second half including the decisive score by Terry Bouhraoua with less than two minutes left.
Canada will play Zimbabwe on Sunday in the quarter-final of the consolation Bowl competition.
Defending champion South Africa defeated the U.S., Kenya and Wales, with Cecil Afrika becoming the Blitzboks' all-time leading points scorer in the process. The hosts will play England in the Cup quarter-finals.
New Zealand, which also conceded just seven points, won Pool D, beating Samoa, Japan and England and will play the U.S. in the Americans' first Cup quarter-final of the season. Current Series leaders Fiji faces Australia while Argentina plays Scotland in the other two quarter-finals.
The South Africa event is the third stop on the IRB circuit.