Seven-time champion Rafael Nadal and world number one Novak Djokovic, who are seeded to meet in the semi-finals, aim to bring that showdown a little closer on Thursday.
Nadal, bidding to become the first man to win the same major eight times, faces Slovakia's Martin Klizan for a place in the last 32.
Nadal, the third seed and 11-time Grand Slam winner, was given a major fright in the first round against Daniel Brands.
The German took the first set and was a 3/0 up in the second set tiebreaker before the champion rallied to take his Paris record to 53 wins in 54 matches.
Top seed Djokovic, beaten by Nadal in the 2012 final, and needing a French Open title to become just the eighth man to complete the career Grand Slam, faces Argentina's Guido Pella, the world number 83, for a place in the third round.
In the women's tournament, defending champion Maria Sharapova takes on Canadian teenager Eugenie Bouchard, the junior Wimbledon champion.
Chinese sixth seed Li Na, the 2011 champion, faces America's Bethanie Mattek-Sands.