Frenchman Tricole, making his bow at the BDO World Championships, dispatched a double eight to finish with a 76.
Montgomery, ranked 25th in the world and winner of the 2019 Czech Open, threw five maximums, had an average of 92.59 and had a match dart but fell to debutant Tricole.
Elsewhere, Darren Herewini beat Simon Stainton 3-1 in a preliminary encounter.
Darts player withdraws from virtual event due to bad wi-fi
Simon Stainton makes the maximum... much to the delight of the BDO crowd
Herewini fought back from a set down on the back of an average of 87.30 to set up an encounter with 12th seed Andy Hamilton.
Beau Greaves, 15, made an impressive start to her BDO World Championship debut, besting Tori Kewish 2-0 to progress to the quarter-final stage.
Greaves, won four senior titles to qualify for the BDO's blue riband event, produced two maximums and finished with an average of 80.37 to underline her credentials as one of the game's top prospects.
"I've had a really good year, I'm just having a bit of fun and seeing how far I can get in this tournament," said Greaves after the match.
BDO World Professional Championship
(11) Mario Vandenbogaerde (BEL) 3 vs 0 Sebastian Steyer (POL)
Justin Thompson (AUS) 3 vs 0 Scott Williams (ENG)
Vicky Pruim (SWE) 0 vs 2 Corrine Hammond (AUS)
(4) Dave Parletti (ENG) 2 vs 3 Chris Landman (NTH)
Darren Herewini (NZ) 3 vs 1 Simon Stainton (ENG)
(6) Beau Greaves (ENG) 2 vs 0 Tori Kewish (AUS)
Thibault Tricole (FRA) 3 vs 2 Ross Montgomery (SCO)
PDC takes video route with home competition announcement
Fallon Sherrock draws on Premier League darts debut