Gasquet eased past Denis Istomin of Uzbekistan 6-4, 6-2 and will be bidding for his 11th career title and first since Moscow in October 2013. Lopez reached his second final in two weeks by defeating American Sam Querrey 6-4, 7-6 (4). He will be chasing his fourth title and first since winning at Eastbourne last year.
The 19-year-old Keys — the youngest player in the top 50 — fought off three break points before taking the opening set with a single break.
"I definitely think I served well ... (it) got me back in some games," Keys said. "Then I think I just returned well a couple of games, and that was really the match."
Chasing her fourth career title, Kerber reached her second Aegon International final with a 3-6, 7-6 (3), 6-3 victory over 2009 champion Caroline Wozniacki.
Fifth-seeded Kerber, who finished as runnerup to Tamira Paszek in 2012, challenged her Danish opponent throughout the match which featured fiercely contested baseline rallies.
Kerber held a set point at 5-4 before winning the last six points of the tiebreaker to claim the second set, and in the third she finished strongly by sweeping five of the last six games.
Wozniacki's engagement to golfer Rory McIlroy ended last month. After Friday's match she said: "You know, sometimes life throws you things that you didn't expect, but you just have to embrace it and move forward. It makes you stronger. I'm in a good place right now."