Davydenko downed top-seeded 6-foot-9 American John Isner 6,4, 7-6 (7-4) and Simon defeated Brazilian qualifier Thomaz Bullucci 7-5, 6-0 at the Nice Lawn Tennis Club.
Reigning champion Almargo of Spain, the No. 3 seed, beat Belgian Steve Darcis 6-4, 6-4 on the red clay in a tune-up for Sunday's start of the French Open in Paris.
American qualifier Brian Baker, who upset fourth-seeded Frenchman Gael Monfils Wednesday, plays Mikhail Kukushin of Kazakhstan in another quarterfinal match.
Monfils pulled out of the French Open Thursday with a knee injury.
The winner of the $505,000 Nice Open takes home $91,000.
2014: The Year in Music [PHOTOS]