The No. 4-seeded Radwanska, last year's Wimbledon runner-up, played for the first time since withdrawing before last week's Brussels tournament with a right shoulder injury.
Playing in sunny, mild weather on Court Suzanne Lenglen, Radwanska committed only eight unforced errors.
Radwanska has won two tournament titles this year but is just 2-2 on clay this spring. She has never advanced beyond the fourth round at Roland Garros.
Her sister, Urszula, beat 30th-seeded Venus Williams in the final match Sunday, 7-6 (5), 6-7 (4), 6-4
No. 15 Roberta Vinci won in less than an hour Monday morning, beating Stephanie Foretz Gacon 6-3, 6-0.