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Bartoli, a former Wimbledon finalist, lost to Camila Giorgi 6-3, 6-2 and Paszek was beaten by French wild-card entry Virgine Razzano 6-1, 6-4.
Bartoli dropped her serve six times in the match against the 88th-ranked Italian, who had four aces.
Also, sixth-seeded Christina McHale lost to Lauren Davis 7-5, 6-3, while Eugenie Bouchard, Johanna Larsson, Lucie Hradecka, Magda Linette and Shelby Rogers all advanced.
Heavy rain prevented any play on Monday, forcing seven first-round matches to be moved to Tuesday.
Meanwhile, Chanelle Scheepers fought her way into the second round seeing off Claire Feuerstein of France 7-5, 6-4.
Results from the second day of the WTA Strasbourg Open (x denotes seeding):
First Round:
Camila Giorgi (ITA) bt Marion Bartoli (FRA x1) 6-3, 6-2
Eugenie Bouchard (CAN) bt Silvia Soler (ESP) 6-3, 6-3
Anna Tatishvili (GEO) bt Caroline Garcia (FRA) 6-7 (4/7), 7-5, 6-4
Monica Niculescu (ROM x5) bt Marina Erakovic (NZL) 6-7 (7/9), 6-3, 7-6 (7/5)
Alize Cornet (FRA x3) bt Mathilde Johansson (FRA) 6-3, 6-2
Magda Linette (POL) bt Olga Puchkova (RUS) 6-4, 7-6 (7/2)
Shelby Rogers (USA) bt Marta Domachowska (POL) 6-2, 7-5
Chanelle Scheepers (RSA x7) bt Claire Feuerstein (FRA) 7-5, 6-4
Mara Teresa Torr (ESP) bt Daniela Hantuchova (SVK x8) 6-3, 4-6, 7-6 (7/4)
Flavia Pennetta (ITA) bt Elina Svitolina (UKR) 6-4, 6-2
Misaki Doi (JPN) bt Karolna Plskov (CZE) 7-5, 6-2
Lauren Davis (USA) bt Christina McHale (USA x6) 7-5, 6-3
Lucie Hradeck (CZE) bt Garbie Muguruza (ESP) 6-4, 6-3
Johanna Larsson (SWE) bt Petra Cetkovsk (CZE) 6-2, 2-6, 6-3
Virginie Razzano (FRA) bt Tamira Paszek (AUT x2) 6-1, 6-4
