Laura Robson set up a second round clash against Caroline Wozniacki at Eastbourne after beating Yulia Beygelzimer.
British number two Heather Watson won her first WTA Tour match since February at the Aegon Classic in Birmingham.
Johanna Konta's run at the Aegon Trophy continued after a 6-2 5-7 7-5 quarter-final win over Alison Riske in Nottingham.
Dan Evans set up an all-British second round battle with Brydan Klein at the Aegon Trophy in Nottingham.
Johanna Konta cruised into the second round of the Aegon Trophy while Anne Keothavong went out to Tamira Paszek.
World number six Li Na will warm-up for Wimbledon at the Aegon International in Eastbourne.
Maria Sharapova started her French Open title defence with a ruthless 6-2 6-1 dismissal of Taipei's Hsieh Su-Wei.
The full schedule for the second day at Roland Garros, with defending champion Rafa Nadal in action.
Draw for the French Open women's singles first round (prefix number denotes seeding): 1-Serena Williams (U.S.) v Anna Tatishvili (Georgia) Qualifier v
Round-up: Top two seeds Marion Bartoli and Tamira Paszek were bounced out of the opening round in Strasbourg in straight sets.
The player field has been announced for the Aegon Classic, staged on grass courts in Birmingham from June 9-16.
British No.1 Laura Robson will play in the Aegon International in Eastbourne ahead of Wimbledon.
American teenager Madison Keys was immersed in her algebra homework when she got the message that she was due on court in 10 minutes to play fifth seed and
Top seed Marion Bartoli bowed out of the Oeiras Open in Estoril in the first round after losing 0-6 6-1 4-6 to Shuai Peng.
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