Jacqueline Cristian had former doubles partner Sofia Kenin on the ropes, but the Australian Open champion emerged triumphant in Lyon.
Chloe Paquet dominated Kristina Mladenovic in the first set, but the second seed rallied to reach the second round in Lyon.
Ons Jabeur pushed Simona Halep all the way, but the two-time grand slam champion was not to be denied a place in the last eight in Dubai.
We take a look at the best first-round matches at the Australian Open, including Venus Williams' meeting with Coco Gauff.
Ashleigh Barty was unable to inspire Australia as France claimed their third Fed Cup title with a 6-4 6-3 win in a deciding doubles match.
The first day of the Fed Cup final delivered two lopsided rubbers as Ashleigh Barty and Kristina Mladenovic shone in the Perth sunshine.
The door is open for Belinda Bencic to qualify for the WTA Finals after Kristina Mladenovic's defeat of Kiki Bertens in Moscow.
Camila Giorgi, Alison Van Uytvanck and Fiona Ferro were the three seeds to tumble at the Luxembourg Open on Tuesday.
Maria Sakkari's withdrawal gave Coco Gauff another chance at the Linz Open and the lucky loser took full advantage.
Naomi Osaka made it six wins in succession as world number one Ashleigh Barty and defending champion Caroline Wozniacki triumphed in China.