Querrey broke Mathieu twice and served an ace to take the first set.
Querrey will play another Frenchman in the next round, either second-seeded Gilles Simon or Kenny De Schepper.
Carlos Berlocq of Argentina and Frenchmen Nicolas Mahut and Albano Olivetti moved into the second round with straight-set wins.
Berlocq, who won the Swedish Open in July, did not face any break points in his 6-3, 6-4 victory over Jiri Vesely of the Czech Republic, while Mahut beat Leonardo Mayer of Argentina 7-6 (2), 6-4.
Wild card Olivetti defeated 2010 runner-up Mischa Zverev of Germany 7-5, 7-6 (3).
Mahut won two titles in the summer and is enjoying his best season.
He blew a 4-2 lead in the first set but still won the tiebreaker before breaking Mayer in the opening game of the second set.
Ranked 254th in the world, Olivetti saved four break points in the first set and fired a total of 20 aces.
In his return from a knee injury, top-seeded Jo-Wilfried Tsonga was set to play Edouard-Roger Vasselin in an all-French match later on Wednesday.
Results from the third day of the ATP Metz Open on Wednesday (x denotes seeding):
Tobias Kamke (GER) bt Marton Fucsovics (HUN) 1-6, 6-3, 6-2
Sam Querrey (USA x6) bt Paul-Henri Mathieu (FRA) 6-2 - retired
Carlos Berlocq (ARG) bt Jir Vesely (CZE) 6-3, 6-4
Albano Olivetti (FRA) bt Mischa Zverev (GER) 7-5, 7-6 (7/3)
Nicolas Mahut (FRA) bt Leonardo Mayer (ARG) 7-6 (7/2), 6-4