Olympic champions Fiji could only finish ninth - their lowest ever placing in Dubai in series history - after agonisingly missing out on a Cup quarter-final place on points difference in their pool.
The three teams all won two matches and lost one to finish on seven points, but France and Argentina's points difference, at plus-28 and plus-27, respectively, were better than that of Fiji's, at plus-14.
The defeat was also Fiji's first in the pool stages in Dubai since losing to England nine years ago. New Zealand play US while Australia is up against Samoa in other Cup quarters showdown. Australia beat US 24-12 to top Pool B, while New Zealand were more comfortable 40-7 winners over Samoa in the Pool C decider.
The results mean the All Blacks Sevens will now play the US in the Cup quarter-finals tonight at 8:35pm.
Pool "D" winners South Africa, who beat England 19-14, face Argentina while England take on France in the Cup quarters.
While Fiji and Canada, as the two best third-placed teams, to meet in the ninth place play-off, the 11th place play-off will be contested by the other teams to finish third in their pools, Ireland and Spain.
Australia scored the opening three tries in rushing past the USA 24-12, and New Zealand enjoyed romps against Canada and Samoa on day two of the three-day event.
New Zealand has won the World Series event in Dubai, beating Canada 17-14 in the final.
The win sees South Africa top the Series standings with 22 points.
There is better news however for Samoa who will meet Australia in the Cup quarter-finals.
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