Shapovalov made a brisk start and raced to a 3-0 lead before Gasquet responded with a mix of aggressive backhands and clever drop shots to reel off five consecutive games.
Top seed Rafael Nadal's bid for a maiden Paris Masters title was halted on Saturday when the Spaniard was beaten 6-4, 7-5 in the semi-finals by German fourth seed Alexander Zverev.
World No 2 Djokovic, who received a first-round bye, broke his opponent's serve four times to extend his winning run to 19 matches.
Rohan Bopanna and his Australian partner Matthew Ebden have clinched a spot in the prestigious season-ending ATP Finals, marking the Indian's fourth appearance in the tournament.
The 32-year-old, who has not played since retiring injured in the US Open semi-finals, cited an abdominal injury.
Federer, Nadal and Djokovic had made it near impossible for their peers to live, and thrive, amongst them. But the coming generation, which hasn't been as scarred by defeat at the hands of the Big 3, may make tennis unpredictable again.
"It has been an amazing year. One year ago, for sure I never dreamed about being World No. 1 again at the end of the season. It's something that means a lot to me. But the season is not over."
Iran were banned from an Olympic football qualifying match against Jordan later that year after refusing to remove their hijabs before kick-off.
Serbian former world number one Novak Djokovic will be in action at his home club, working under old coach Marian Vajda -- desperately searching for some spark after tumbling down to 13th in the rankings.
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