The first day started well for the Romanian team after tennis star Simona Halep took all the positive energy given by the unbelievable Romanian supporters and used it to fuel her game and beat Kristina Mladenovic.
France, who won the competition in 1997 and 2003, will visit Australia in the November 9-10 final.
While Belarus are bidding to reach the final for the second time in three attempts, after being beaten by the United States in 2017, Australia are targeting their first decider in 26 years.
Mladenovic did well to offer some resistance late in the opening set before breaking Halep's serve at the start of the second, but the 2018 French Open victor swiftly regained control to ease to victory.
Jarry saved a match point in a tense final set that swung one way and the other before the Chilean outsider held it together in a decisive tie-break to claim the biggest win of his career.
A fifth rubber was needed for the semi-final after both nations won one singles matches each on Sunday, and Halep stepped up to play her first Fed Cup doubles match in two years due to an injury to Irina-Camelia Begu.
"Every match was incredible", said delighted France captain Julien Benneteau. "But now we will have a good night". 'It was really hard to start the match because of the emotions, reigning Roland Garros champion Halep 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.
After almost three hours of fantastic tennis and score changes, Halep returned the fate of the game with Caroline Garcia in her favor, and won the match 6-7 (6), 6-3, 6-4.
"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".