Nadal will take on fellow Spaniard and 17th seed Roberto Bautista-Agut for a place in the last eight while defending champion Novak Djokovic faces Spain's Albert Ramos-Vinolas.
In the women's draw, Spanish holder Garbine Muguruza faces local hero Kristina Mladenovic on Suzanne Lenglen Court while 10th-seeded Venus Williams takes on Swiss Timea Bacsinszky.
Among the third round matches to be completed are that of eighth seed Kei Nishikori, who won the first two sets but was saved by the rain as talented South Korean Chung Hyeon pulled one set back and led 3-0 in the fourth.
The third-round battle between France's top title contenders will also resume with 15th-seed Gael Monfils leading 6-5 in the first set against Richard Gasquet, while American John Isner, the 21st seed, is a set down against Russia's Karen Khachanov.
Four women's singles third round encounters still need to be played, including Czech second seed Karolina Pliskova against Germany's Carina Witthoeft and Ukrainian fifth seed Elina Svitolina versus Poland's Magda Linette.
(Reporting by Karolos Grohmann; editing by Ken Ferris)
