The German former world number one, seeded 12th, played from the back of the court throughout the match, making it impossible for her 24-year-old opponent to develop her attacking game.
Double Grand Slam champion Kerber will next face world number one Simona Halep after the Romanian demolished Belgian Elise Mertens 6-2 6-1.
Kerber only hit 11 winners but Garcia made 36 unforced errors, meaning the German was never under too much pressure.
Garcia had reached two semi-finals in top-tier events on clay this season, but in front of her home fans on Court Suzanne Lenglen she was unable to produce her best tennis.
The Frenchwoman briefly threatened a comeback when she pulled a break back for 5-3 after saving four match points, but then sent a routine forehand wide on the fifth match point in the following game.
"I'm happy to be through, she has played really well in the last few months," Kerber said of Garcia, who had reached the quarter-finals last year.
All of the French players in the men's singles draw were knocked out of the tournament before reaching the fourth round.
(Reporting by Julien Pretot; Editing by Ken Ferris)
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