The 31st-ranked American, who is seeded sixth in Metz, got off to a slow start but managed to force a tiebreaker in the second set and pull through in the only first-round match of the day.
The match featured 37 aces, including 25 from the 34-year-old Karlovic.
Querrey comes into the tournament after a disappointing second-round exit at the U.S. Open.
Defending champion Jo-Wilfried Tsonga is seeded No. 1 and has a bye into the second round.