Kubot, the 31-year-old world number 30, defeated French 25th seed Benoit Paire 6-1, 6-3, 6-4 while De Schepper, the 26-year-old world number 80, beat Argentine 22nd seed Juan Monaco, 6-4, 7-6 (10/8), 6-4.
Croatian 10th seed Marin Cilic joined the list of Wimbledon's walking wounded on Wednesday when he withdrew with a left knee injury.
Arnaud Clement has been named as France's new Davis Cup captain, the French Tennis Federation (FFT) announced on Friday.