Davydenko, ranked fifth in the world, jumped out to a one-set advantage, taking the set, 6-4. But world No. 81 Florent Serra rallied with a vengeance, losing just two games the rest of the match in ousting Davydenko, 4-6, 6-1, 6-1.
Davydenko was one of five seeded players to lose first-round matches in the tournament.
Almagro lost 7-6 (7-1), 6-4 to Werner Eschauer and Gicquel was a 6-3, 6-4 loser to qualifier Steve Darcis.
Playing more to form, second-seeded Mikhail Youzhny beat Martin Vassallo Arguello, 6-2, 7-5; No. 3 Carlos Moya stopped Christophe Rochus, 6-2, 6-3; and fourth-seeded Filippo Volandri got by Oscar Hernandez, 6-2, 6-4.
Also Tuesday, Sergio Roitman was a 7-6 (7-5), 6-1 winner over Jeremy Chardy; Igor Andreev cruised by Janko Tipsarevic, 6-1, 6-1; Thiemo de Bakker nipped Nicolas Massu. 7-6 (9-7), 7-6 (7-5); and Raemon Sluiter took out Luis Horna. 3-6, 7-5, 6-3.