The two 25-year-olds defeated world number two Simona Halep and Monica Niculescu 5-7 6-3 6-4 to wrap up the tie in front of an enthusiastic home crowd in the Normandy city of Rouen, ending Romania's dreams to reach their maiden final.
France, who won the competition in 1997 and 2003, will visit Australia in the Nov. 9-10 final.
Earlier on Sunday Australia, inspired by in-form Ashleigh Barty, defeated Belarus 3-2 in the other semi-final in Brisbane.
Halep and Niculescu began in dazzling fashion, taking the opening set but the French pair replied in style, levelling the score after striking 25 winners in the second set.
The French duo won on their first match point to seal the rubber and the tie as Niculescu thumped a service return into the net.
Garcia and Mladenovic were playing together for the first time since they were defeated by the Czech Republic in the deciding doubles of the 2016 Fed Cup final.
"Every match was incredible," said delighted France captain Julien Benneteau.
"It was always my intention as captain to put them together and no, it was not hard to do it. The final will be a massive challenge for us, with nothing to lose. But now we will have a good night."
Halep had earlier given the Romanians a 2-1 lead as she needed all her skill and determination to battle past aggressive baseliner Garcia 6-7 (6) 6-3 6-4 in a thrilling encounter that lasted two hours and 21 minutes.
"I knew it would be more difficult than yesterday," the reigning Roland Garros champion said. "She started very fast, hitting the ball very strong, and I think I was a bit slow."
The Romanians, who won their only previous Fed Cup tie against France in 1976, made it to the last four after upsetting defending champions Czech Republic in an epic quarter-final in Ostrava in February.
Pauline Parmentier 6-3 2-6 6-2, who had won just one of her eight Fed Cup rubbers, beat Irina Begu 6-3 2-6 6-2 to send the tie to the decider with the Romanian struggling with an ankle injury in the third set.
"I found out I was playing last night," said Parmentier. "I didn't sleep very well, and I was awake pretty early, ready to play.
"This is my best ever Fed Cup singles match. It's an amazing feeling."
(Reporting by Angel Krasimirov; Editing by Christian Radnedge)
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