Alcaraz, fresh from defeating Djokovic in the Wimbledon final, eased past Hady Habib of Lebanon while Swiatek enjoyed a straight-sets win against Irina-Camelia Begu.
Nadal, who has been carrying a thigh strain, will take on Djokovic for the 60th time if he gets past Marton Fucsovics of Hungary on Sunday.
He warmed up for that clash by partnering Alcaraz to a 7-6 (7/4), 6-4 win over Maximo Gonzalez and Andres Molteni of Argentina.
It was the players’ first match as a pair as Nadal, with his right thigh bandaged, started his bid for a second doubles gold after Rio in 2016, having also captured singles gold in Beijing in 2008.
The torrential rain which swamped the opening ceremony on Friday also brought havoc to Roland Garros, where play on the outside courts was wiped out.
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