Djokovic, a native of Serbia and the No. 3 seed in this French Open warm-up, beat Spanish qualifier Santiago Ventura, 6-2, 6-2.
Robredo topped fellow Spaniard Albert Montanes, 6-4, 6-3.
Montanes was last week's runner-up at the Grand Prix Hassan II tournament in Casablanca, Morocco.
Qualifier Olivier Patience of France beat fourth seed and 2003 Estoril Open winner Nikolay Davydenko, 7-5, 6-1; Guillermo Garcia-Lopez beat sixth-seeded Dmitry Tursunov of Russia, 6-4, 6-3; Juan Monaco of Argentina downed American Sam Querrey, 3-6, 6-1, 6-4; and Paul-Henri Mathieu easily beat Russian Igor Kunitsyn, 6-2, 6-1.