Lopez, 24, who had to win two matches on Friday due to rain earlier in the event, played a tough match against Marin Cilic before a 7-6 (7-2), 6-7 (5-7), 6-3, victory.
Lopez was competing in his first semifinal since August 2005 and reached the fourth final of his career. His lone title came at Vienna in 2004.
Gasquet, 20, defeated German Philipp Kohlschreiber, 6-1, 1-6, 6-2. He has won nine of his last 10 matches, including a title defense at Nottingham last month. His lone loss in that stretch was a first-round defeat at Wimbledon by Roger Federer.
Gasquet, who beat defending champ Gaston Gaudio on Friday, reached the fifth final of his career. He has two titles, both at Nottingham.
Celebrity Families of 2014 [PHOTOS]