Garcia, 19, gave Maria Sharapova a run for her money on her previous appearance on centre court at Roland Garros two years ago but found top seed Williams in an unforgiving mood.
Williams roared into a 5-0 lead in the opening set before Garcia, ranked 114 in the world, held serve to generous applause from the crowd who had earlier witnessed victories for Frenchmen Jo-Wilfried Tsonga and Gael Monfils.
There was precious little hope of a hat-trick of home wins on Chatrier though with Williams, who came into the match on a career-best 25-match winning streak, wrapping up the opening set in 27 minutes.
Garcia offered more resistance in the second set but was still no match for the 15-times grand slam champion who looks in the mood to add to her single French Open title.
Williams faces Romania's Sorana Cirstea in the third round.
A cacophony of noise on Chatrier Court signalled the belated appearance of women's third seed Victoria Azarenka as the Belarusian eased to the second round.
The stadium was barely one third full as Azarenka went through her paces but the low decibel level from the crowd on another chilly day in Paris was countered by the grunts, howls and groans coming from the two players.
Azarenka just about won the noise battle, although Russian Elena Vesnina ran her close, and she had little trouble winning the match either, going through 6-1 6-4.
Incredibly making her eighth main draw appearance at the French Open despite still being only 23, Azarenka had to wait until the fourth day to begin her challenge after rainy weather on Tuesday meant her first-round match was cancelled.
She now faces the prospect of seven matches in 11 days if she is to win the title here.
The twice Australian Open champion has never shone in Paris, with her best performance being quarter-finals in 2009 and 2011.
"It was great to start and there some tough points, especially for a first round match," Azarenka, who was briefly troubled in the second set, said on court before declaring her love for Paris.
She will face Germany's Annika Beck in the second round.
Former world number one and 10th seed Caroline Wozniacki suffered a surprise 7-6(2) 6-3 to unseeded Bojana Jovanovski.
Denmark's Wozniacki looked set for a decent run at Roland Garros after taming British number one Laura Robson in the first round, but she was disappointing against the Serb, who faces Russia's Svetlana Kuznetsova next.
Czech seventh seed Petra Kvitova advanced into the second round after fighting off local wildcard Aravane Rezai's bold challenge in a 6-3 4-6 6-2 victory on Court Suzanne Lenglen.
Polish hopes of a third-round meeting between the Radwanska sisters vanished after the fourth-seeded Agnieszka beat American Mallory Burdette 6-3 6-2 but Urszula went out 6-3 6-3 to German Dinah Pfizenmaier.
1-Serena Williams (U.S.) beat Caroline Garcia (France) 6-1 6-2
4-Agnieszka Radwanska (Poland) beat Mallory Burdette (U.S.) 6-3 6-2
5-Sara Errani (Italy) beat Yulia Putintseva (Kazakhstan) 6-1 6-1
8-Angelique Kerber (Germany) beat Jana Cepelova (Slovakia) 6-2 6-2
Bojana Jovanovski (Serbia) beat 10-Caroline Wozniacki (Denmark) 7-6(2) 6-3
14-Ana Ivanovic (Serbia) beat Mathilde Johansson (France) 6-2 6-2
15-Roberta Vinci (Italy) beat Galina Voskoboeva (Kazakhstan) 6-4 4-6 6-2
Petra Cetkovska (Czech Republic) beat 19-Anastasia Pavlyuchenkova (Russia) 7-5 2-6 6-4
20-Carla Suarez Navarro (Spain) beat Shelby Rogers (U.S.) 3-6 6-4 6-4
26-Sorana Cirstea (Romania) beat Johanna Larsson (Sweden) 6-1 6-4
29-Varvara Lepchenko (U.S.) beat Elina Svitolina (Ukraine) 7-6(5) 6-1
32-Sabine Lisicki (Germany) beat Maria Teresa Torro (Spain) 6-4 6-0
Virginie Razzano (France) beat Zuzana Kucova (Slovakia) 4-6 6-2 6-0
Dinah Pfizenmaier (Germany) beat Urszula Radwanska (Poland) 6-3 6-3
Monica Puig (Puerto Rico) beat Madison Keys (U.S.) 6-4 7-6(2)
3-Victoria Azarenka (Belarus) beat Elena Vesnina (Russia) 6-1 6-4
7-Petra Kvitova (Czech Republic) beat Aravane Rezai (France) 6-3 4-6 6-2
12-Maria Kirilenko (Russia) beat Nina Bratchikova (Portugal) 6-0 6-1
Kaia Kanepi (Estonia) beat 23-Klara Zakopalova (Czech Republic) 7-6(3) 6-2
Jamie Hampton (U.S.) beat 25-Lucie Safarova (Czech Republic) 7-6(5) 3-6 9-7
Anna Karolina Schmiedlova (Slovakia) beat Yanina Wickmayer (Belgium) 7-6(5) 2-6 6-2
Stefanie Voegele (Switzerland) beat Heather Watson (Britain) 6-4 2-6 6-4
Peng Shuai (China) beat Camila Giorgi (Italy) 6-4 6-2
Annika Beck (Germany) beat Sandra Zahlavova (Czech Republic) 6-2 6-1
- Sports & Recreation
- Victoria Azarenka
- Caroline Wozniacki