Averill lead his team with 20 points, but dropped a tight match 3-2 in the first leg of the 2nd Round.
Chaumont put forth a nearly perfect performance against Viking of Norway to move to the 2nd Round.
Poitiers got an upset win over Chaumont to start the season.
The Americans secured the Pool C title with its fifth-straight win on Tuesday, topping Tunisia via sweep. Serbia meanwhile edged out Russia in five sets to claim the second spot in the group.
Multiple upsets took place in the first leg of the round of 12 in the male champions league, including 3 matches that went to 5 sets.
What will the new season hold for the Chaumont 52 side after winning the French Ligue A championship in 2016-2017.