The 23rd seed, who also made it to the last eight in 2008, 2009 and 2011, blazed through the first two sets and held off the world number 41 in the third, ending the contest on a sun-drenched court Philippe Chatrier with an ace.
Monfils will face British seventh seed Andy Murray for a place in the last four, a stage he reached in 2008 when he was defeated by Roger Federer.
"In the third set, when I broke him he started to go for his shots and played more freely," Monfils, whose preparations have been hampered by an ankle injury he sustained in early April, said courtside.
"I became too defensive so I had to accelerate again."
No French man has won their home slam since Yannick Noah in 1983.
During the first two sets, Garcia-Lopez was a pale shadow of the player who knocked out world No.3 Stan Wawrinka in the first round.
The Spaniard peppered the court with unforced errors, most of them from his forehand, the very shot that helped him progress to the last 16.
He went 2-0 down in the third before regaining his composure as Monfils, the last French player left in the singles, played too conservatively.
The Frenchman, who had advanced to this round after beating Italian Fabio Fognini in an unforced errors-fest, turned the situation around thanks to some fine returns and, spurred on by the crowd, broke decisively in the 11th game.
Next up is Wimbledon champion Murray, who fought hard to beat Spain's Fernando Verdasco in straight sets.
"He's such an entertainer," Murray said after his match.
"He is one of my favourite players to watch. There's going to be some fun points."
(editing by Mark Meadows)
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