Netherlands' dream run in the Fed Cup ended agonisingly short of the final when they lost the deciding doubles rubber of a thrilling semi-final against France in Trelaze.
Mladenovic and Garcia then teamed up to beat Bertens and Richel Hogenkamp, coming from a set down to win 4-6, 6-3, 6-3 in a nail-biting climax to the weekend.
France have reached their first final since 2005 where they will be up against the Czech Republic, who also needed a final doubles rubber to win in Switzerland.
The Netherlands were unbeaten since 2013 despite a team full of lower-ranked players, beating Australia last year to reach the World Group and stunning Russia in the first round.
Karolina Pliskova and Lucie Hradecka booked the Czech Republic's place in a fifth Fed Cup final when they beat Swiss duo Martina Hingis and Viktorija Golubic 6-2 6-2.
Golubic, ranked 129 in the world, had kept the Swiss in the hunt with two singles wins.
Four-times champions Italy were relegated from the World Group for the first time in 18 years after losing 4-0 in a playoff with Spain who return to the elite after a two-year absence.
Belarus caused an upset by beating Russia 3-1 in their World Group playoff, meaning the Russians are also relegated from the top group for the first time in 18 years.
Image: Kristina Mladenovic of France
Photograph: Zak Kaczmarek/Getty Images
Indian junior Fed Cup team qualifies for World Group
Australian Open champion Kerber advances in Miami heat
Manavjit, Chenai get off to good start at Shooting World Cup
Sharapova set to make 'major announcement'
Maggi Noodles: Reclaiming faith in an instant