Rain again caused delays and pushed back play, but all except four Thursday matches were completed. One of those still undetermined had world No. 1 Maria Sharapova leading Bethanie Mattek, 6-2, 2-3. Sharapova had broken Mattek's serve when play was stopped because of darkness.
Jankovic, seeded third, was a 6-2, 7-6 (7-5) winner over Marina Erakovic; Kuznetsova ran past Vania King, 6-4, 6-2; Dementieva routed Marta Domachowska, 6-1, 6-4; and Williams, seeded eighth, had a seemingly easy 6-2, 6-4 win over Selima Sfar.
The mood of the French crowd was doused with the loss by local favorite Amelie Mauresmo to qualifier Suarez Navarro, 6-3, 6-4.
Also winning Thursday were 12th-seeded Agnes Szavay, No. 13-seeded Dinara Safina, 16th-seeded Victoria Azarenka, 18-seeded Francesca Schiavone, 19-seeded Alize Cornet, 26th-seeded Flavia Pennetta, No. 27-seeded Katarina Srebotnik; and 28th-seeded Dominika Cibulkova ran by Milagros Sequera, 6-3, 6-0.
A very mild upset came when Olga Govortsova grounded 31st-seeded Ai Sugiyama, 6-0, 7-5. Casey Dellacqua, Iveta Benesova and Petra Cetkovska also won second-round matches Thursday.
Celebrity Families of 2014 [PHOTOS]