Both Frenchmen enjoyed straight-sets victories while compatriot Jo-Wilfried Tsonga had his match delayed by rain in the final action of the day’s first round.
Monfils needed just over an hour to dispatch Fabio Fognini 6-3 6-1, denying the Italian a single break in the match.
“I wanted to start off this tournament well. It was not a great match, but I didn’t play bad,” Monfils told reporters. “I played a solid match. It was important to me.”
Ninth-seeded Simon extended his perfect record against Andreas Seppi to 5-0 with his 6-2 6-4 victory.
Simon broke Seppi three times and he too never lost serve.
Tsonga was leading his opening set against Croatia’s Borna Coric 2-1 when play was suspended.
Defending champion Tsonga has fallen to number 24 in the world, his lowest ranking since bursting onto the scene following the 2008 Australian Open.
In other games, Spain’s Tommy Robredo overcome Feliciano Lopez 6-3 3-6 6-3, American Sam Querrey beat Martin Klizan 6-3 6-3, and Croatian Ivo Karlovic fired 18 aces past Poland's Jerzy Janowicz on the way to a 6-4 7-6(6) victory.
Novak Djokovic, Rafa Nadal and Andy Murray all had first-round byes.
(Writing by Jahmal Corner; Editing by Peter Rutherford)
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