No. 4 seed Kenin blew past Romanian qualifier Irina Bara 6-2, 6-0 in 72 minutes on Court Philippe Chatrier.
Zhang ended the run of French wild-card entry Clara Burel with a hard-fought 7-6 (2), 7-5 win in 2 hours, 12 minutes on Court Simonne Mathieu.
Zhang, 31, is ranked 39th and had never advanced beyond the third round in her nine previous French Opens.
Kenin has advanced to the second week of all three Grand Slams during this pandemic-altered season. She won in Australia and reached the fourth round at the US Open.
Kvitova broke in the match’s opening game when the 100th-ranked Fernandez, the youngest player left in the field, double-faulted. From there, Fernandez took five games in a row for a 5-1 lead.
But Kvitova then woke up and took control, grabbing the first set and a two-break lead at 3-0 in the second.
Kvitova, whose best showing at Roland Garros was a semifinal run in 2016, will face Zhang in the fourth round.