Tsonga, the 2014 champion in Toronto, slumped to a heavy 6-2, 6-2 defeat by German Jan-Lennard Struff while Pouille, with coach Amelie Mauresmo looking on, lost to Canada's Milos Raonic 6-4, 6-4.
The 60th-ranked Tsonga indicated he would now focus on weekend qualifying rounds at the last major tune-up prior to the US Open in Cincinnati.
Australian Open semi-finalist Pouille was shell-shocked after his hammering by Raonic, his fourth from five meetings with the towering Canadian.
"There is really nothing to say about my game - it was not there today," said Pouille.
"There were no rallies, it was nothing special. In these kind of matches, it's only about return and serve.
"It's really, really when he's serving like this, something like 70 per cent first serve. He's really tough to read and to return.
"It was difficult, but I knew it would be like this against Milos."
Pouille had two aces compared to 16 for Raonic, the 2013 finalist here against Rafael Nadal.
Pouille has struggled to regain his game after his career-best Grand Slam run in Melbourne, which was followed in spring by a Roland Garros second round exit.
Though he tried to improve on grass, his best showing was a Stuttgart quarter-final, with a third-round defeat by Roger Federer at Wimbledon.
"This is just the beginning of the second part of the season. I have to keep working, trying to keep pushing hard to come back at my best level."
Results from the ATP Montreal Masters on Monday (x denotes seeding):
Tommy Paul (USA) bt Brayden Schnur (CAN) 6-1, 6-2
Milos Raonic (CAN x17) bt Lucas Pouille (FRA) 6-4, 6-4
Jan-Lennard Struff (GER) bt Jo-Wilfried Tsonga (FRA) 6-2, 6-2
Cameron Norrie (GBR) bt Marton Fucsovics (HUN) 5-7, 6-2, 6-3
Cristian Garin (CHI) bt Laslo Djere (SRB) 6-2, 7-6 (7/4)