Mathieu, a wild-card entrant, won the first five and the last four games of a 6-1, 3-0 decision over Nicolas Mahut. Mahut retired after the third game of the second set, citing the flu.
Mathieu, despite landing just 44 percent of his first serves, lost just 10 points through the five games serving and had four breaks in the five games Mahut served.
He earned a spot in the second round against top-seeded and defending champion Richard Gasquet, who has a first-round bye.
Both Gasquet and Mathieu are French and are among 11 French players in the 32-man field.