Federer swept the final five games against the 60th-ranked Mannarino to win in 1 hour, 12 minutes.
Hampered by back injuries in a difficult season, Federer has won only one title as his ranking has dropped to No. 7. He also has yet to secure a place in the eight-man lineup at the season-ending ATP World Tour finals in London next month.
A five-time champion at Basel, Federer is only seeded third this week and made just 51 percent of his first serves Monday. He needed 13 chances to break Mannarino's serve four times in the match.
The last time he played in Switzerland, Federer fell to a straight-set loss to 55th-ranked German Daniel Brands in his opening match at the Swiss Open in July. Federer said Sunday he is fitter and more confident now, and broke Mannarino's serve to begin the match. Still, he double-faulted to lose his second service game.
Settling into his rhythm, Federer broke again to lead 4-3 and converted his first set point with a forehand winner.
Mannarino, who lost to Federer in the third round of the U.S. Open, sent a two-handed backhand long to concede a 3-2 lead in the second set. Federer broke serve again by hitting another forehand winner and clinched the match with a serve that Mannarino could not return.
Earlier Monday, Lukasz Kubot of Poland beat Daniel Gimeno-Traver of Spain 7-5 (6), 6-2, and Tobias Kamke of Germany beat Victor Hanescu of Romania 6-4, 6-4.
Alexandr Dolgopolov of Ukraine was playing Kenny de Schepper of France in the late match.