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The unseeded Frenchman fought back in the third set of their first-round match, but Anderson, South Africa's No 1 player, held onto win 6-4, 6-4, 6-7, 6-3.
A host of South Africans are set to take the court on Wednesday, led by Chanelle Scheepers who comes up against world No 27 Maria Kirilenko of Russia in the second round of the women's singles.
Anderson and Australia's Carsten Bell face Brazilian 11th seeds Marcelo Melo and Bruno Soares in the first round of the men's doubles.
Wesley Moodie and regular partner Dick Norman of Belgium, seeded eighth, take on Juan Sebastian Chabal of Columbia and Eduardo Schwank of Argentina.
Scheepers will pair up with Kai-Chen Chang of Taipei, and the duo face a tough test in their first round match against Kveta Peschke and Katarina Srebotnik of Slovakia, the second seeds in the women's doubles competition.
South Africa's Natalie Grandin and Vladimira Uhlirova of the Czech Republic are up against Canadian Rebecca Marino and Ipek Sinoglu of Turkey.
Results on Tuesday from Roland Garros:
Men
First Round
Alexandr Dolgopolov (21), Ukraine, def. Rainer Schuettler, Germany, 6-3, 6-3, 6-1.
Andy Murray (4), Britain, def. Eric Prodon, France, 6-4, 6-1, 6-3.
Ivan Ljubicic, Croatia, def. Somdev Devvarman, India, 6-4, 6-3, 6-4.
Andreas Haider-Maurer, Austria, def. Ryan Sweeting, United States, 6-1, 6-7 (5), 6-2, 6-0.
Florian Mayer (20), Germany, def. Igor Kunitsyn, Russia, 6-3, 4-6, 6-4, 6-3.
Robin Haase, Netherlands, def. Daniel Gimeno-Traver, Spain, 6-2, 7-6 (3), 6-3.
Juan Ignacio Chela, Argentina, def. Tim Smyczek, United States, 7-6 (5), 6-1, 6-1.
Sam Querrey (24), United States, def. Philipp Kohlschreiber, Germany, 3-6, 6-1, 6-2, 6-4.
Jurgen Melzer (8), Austria, def. Andreas Beck, Germany, 6-3, 6-4, 6-2.
Arnaud Clement, France, def. Filippo Volandri, Italy, 6-3, 1-6, 7-6 (9), 6-4.
Pablo Andujar, Spain, def. Santiago Giraldo, Colombia, 7-6 (5), 6-3, 6-3.
Lukasz Kubot, Poland, def. Nicolas Almagro (11), Spain, 3-6, 2-6, 7-6 (3), 7-6 (5), 6-4.
Rafael Nadal (1), Spain, def. John Isner, United States, 6-4, 6-7 (2), 6-7 (2), 6-2, 6-4.
Robin Soderling (5), Sweden, def. Ryan Harrison, United States, 6-1, 6-7 (5), 6-3, 7-5.
Xavier Malisse, Belgium, def. Dmitry Tursunov, Russia, 7-5, 3-6, 6-3, 3-6, 6-1.
Kevin Anderson (32), South Africa, def. Nicolas Mahut, France, 6-4, 6-4, 6-7 (6), 6-3.
Jeremy Chardy, France, def. Grigor Dimitrov, Bulgaria, 6-2, 6-4, 6-4.
Lukas Rosol, Czech Republic, def. Edouard Roger-Vasselin, France, 3-6, 6-2, 6-4, 3-6, 7-5.
Fernando Verdasco (16), Spain, def. Juan Monaco, Argentina, 6-2, 7-5, 4-6, 6-4.
Women
First Round
Jarmila Gajdosova (24), Australia, def. Virginie Razzano, France, 6-3, 6-1.
Caroline Garcia, France, def. Zuzana Ondraskova, Czech Republic, 6-3, 6-4.
Li Na (6), China, def. Barbora Zahlavova Strycova, Czech Republic, 6-3, 6-7 (6), 6-3.
Anabel Medina Garrigues, Spain, def. Corinna Dentoni, Italy, 7-5, 7-5.
Silvia Soler-Espinosa, Spain, def. Elena Vesnina, Russia, 4-6, 6-3, 6-4.
Ayumi Morita, Japan, def. Kristina Mladenovic, France, 2-6, 6-4, 7-5.
Ekaterina Makarova, Russia, def. Romina Oprandi, Italy, 6-4, 3-6, 6-0.
Maria Sharapova (7), Russia, def. Mirjana Lucic, Croatia, 6-3, 6-0.
Johanna Larsson, Sweden, def. Ana Ivanovic (20), Serbia, 7-6 (3), 0-6, 6-2.
Yanina Wickmayer (21), Belgium, def. Monica Niculescu, Romania, 6-0, 6-3.
Vania King, United States, def. Dominika Cibulkova (22), Slovakia, 6-7 (10), 6-3, 6-2.
Victoria Azarenka (4), Belarus, def. Andrea Hlavackova, Czech Republic, 6-3, 6-3.
Lucie Hradecka, Czech Republic, def. Anastasija Sevastova, Latvia, 6-3, 5-7, 6-1.
Arantxa Rus, Netherlands, def. Marina Erakovic, New Zealand, 2-6, 6-4, 6-4.
Elena Baltacha, Britain, def. Sloane Stephens, United States, 7-5, 6-2.
Alexandra Dulgheru (27), Romania, def. Laura Pous-Tio, Spain, 6-3, 6-4.
Kim Clijsters (2), Belgium, def. Anastasiya Yakimova, Belarus, 6-2, 6-3.
