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.
Federer 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 seeded only 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.