Federer, the 2009 French Open winner who is seeking his first title of 2013, fired 10 aces in dispatching Spanish qualifier Pablo Carreno-Busta 6-2, 6-2, 6-3 in an 80-minute match.
His next opponent will be India's Somdev Devvarman, who logged a 6-3, 6-3, 7-5 decision over Spaniard Daniel Munoz-De La Nava.
Spain's Ferrer won a first-round French Open match for the 11th straight year, moving on with a 6-4, 6-3, 6-4 triumph over Australia's Marinko Matosevic.
Portugal's Joao Sousa, Spaniard Roberto Bautista Agut, Slovenia's Blaz Kavcic and Czech Jan Hajek also posted Day 1 victories.
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