Federer, who used to ball boy at the tournament as a child, raced into a 2-0 lead in the first set but then lost the next two games with a double fault handing Mannarino the break back.
However, Federer was in complete control from that point on and did not even have to face another break point for the rest of the match.
One more break in the first set and two in the second saw him comfortably on his way into the second round.
Federer is seeded third for the tournament behind defending champions Juan Martin del Potro and Tomas Berdych,
Federer has won the tournament a record five times but lost last year's final to del Potro.
He will face Horacio Zeballos or Denis Istomin in the second round.
Federer currently stands in the seventh of eight effective qualifying spots (thanks to the absence of Andy Murray) for the ATP Tour finals, and will hope that results over the next two weeks - in Basel and the Paris Masters - go his way.
A title - or a run to the final - on home turf would all-but-guarantee a place in the season finale in London.
Results from the Basel International Men's Singles Round 1 matches on Monday
3-Roger Federer (Switzerland) beat Adrian Mannarino (France) 6-4 6-2
Lukasz Kubot (Poland) beat Daniel Gimeno-Traver (Spain) 7-6(6) 6-2
Tobias Kamke (Germany) beat Victor Hanescu (Romania) 6-4 6-4
Alexandr Dolgopolov (Ukraine) beat Kenny De Schepper (France) 6-4 6-4