“It gave me the chill, I have to say,” said Boisson. “But it was extraordinary to have the crowd supporting me so much.
“Even though sometimes it’s a bit raucous and there is a lot of noise between two points.”
Boisson had trailed 3-1 and 5-3 in the first set but saved set points to turn the match in her favour.
She kept her cool as last year’s semifinalist Andreeva unravelled from a 3-0 lead in the second set to win the last six games.
A frustrated Andreeva received a warning from the umpire for blasting the ball into the crowd. She was then booed when she argued with the umpire over a line call.
“Obviously I expected it,” said the Russian of the partisan home crowd.
“I think that in the first set I managed it pretty well... but obviously with nerves and with pressure, it became a little harder.”
Andreeva struggled with the pressure, hitting nine double-faults in total, and made 43 unforced errors to Boisson’s 27.
She conceded the final game to love as Boisson wrapped up victory on her first match point.
The player from Dijon advances to meet US world No 2 Coco Gauff, who battled back from a set down to beat Australian Open champion Madison Keys 6-7 (6/8), 6-4, 6-1.
“For sure I will go for the dream, because my dream is to win it, not to be in the semifinal,” warned Boisson.
“My routine won’t change, it’s been the same since the start of the tournament,” she added of her preparation for Thursday’s semifinal.
Former US Open winner Gauff, 21, said she would just pretend the home crowd was “cheering for me”.
“Just using it and not letting that get to you.”
Boisson becomes the lowest-ranked major semifinalist in the past 40 years.
The winner of the Saint Malo tournament on the secondary circuit in 2024 was ranked No 152 before her injury.
“[It] was the toughest moment of my life,” said Boisson, who had only won one match on the main circuit before Roland Garros – at the modest WTA 250 event in Rouen on clay in April.
Her earnings this year have been €18,470 ($21,100) for a career-total €130,000 ($148,000).
Reaching the singles semifinals at Roland Garros will earn her a paycheque of €690,000.
The winner receives €2.55 million and the runner-up half that.
“She’s probably a better player than her ranking right now,” said Andreeva.
“I think that if she keeps playing like this, freely and not being scared or afraid... I think everyone can win.
“It’s going to be pretty interesting to watch. I think if maybe she believes in herself enough, maybe she can.”
Boisson is the third player to reach the semifinals in her Grand Slam main-draw debut since 1980, following Monica Seles and Jennifer Capriati who also did it at Roland Garros in 1989 and 1990.
She becomes the first French semifinalist at her home Grand Slam event since Marion Bartoli in 2011 – and the first in the Open Era to do it as a wildcard.