World number one Ashleigh Barty and last year's runner-up Sloane Stephens lost at the Rogers Cup.
Victoria Azarenka suffered a second-round loss to Donna Vekic at the Silicon Valley Classic.
Venus Williams went down to Bethanie Mattek-Sands in the opening round of the Silicon Valley Classic.
Cori Gauff dispatched Magdalena Rybarikova 6-3 6-3 to move into round three, while Simona Halep and Karolina Pliskova also progressed.
A number of seeds crashed out of the top half of the French Open draw, but Simona Halep, Naomi Osaka and Serena Williams remain in the hunt.
The current world number one faced a former top-ranked star on Thursday and Victoria Azarenka made Naomi Osaka feel like the underdog.
Victoria Azarenka looked set to cause an upset at the French Open but fell to defeat from a set and a break up versus top seed Naomi Osaka.
It is three French Open first-round exits in four years for Jelena Ostapenko, as the 2017 champion's odd Roland Garros record continued.
Johanna Konta celebrated her 28th birthday by reaching the semi-finals of the Internazionali d'Italia in Rome on Friday.
While Simona Halep insisted fitness was not an issue ahead of the French Open, Naomi Osaka eased through at the Internazionale d'Italia.