While Sinner stretched his Grand Slam winning streak to 19 matches after earning back-to-back titles at the US Open last year and the Australian Open in January, Boisson, ranked 361st at the start of the tournament, thrilled the home crowd with a dazzling performance on Wednesday.
Sinner will face the winner between three-time French Open champion Novak Djokovic, hunting a record-breaking 25th singles Grand Slam, and Germany's third seed Alexander Zverev in the last four.
Sinner, who beat Bublik in straight sets, is the first Italian man to reach six Grand Slam semi-finals.
The 23-year-old, who served a three-month doping ban before returning to action in Rome last month, raced through the first set after twice breaking the Kazakh, who had stunned fifth seed Jack Draper in the previous round.
Looking to become the first man representing Kazakhstan to defeat a world No 1, Bublik, who hit 37 drop shots against Draper, pulled out this weapon again in the second set.
But Sinner broke and held to take it. Ever the entertainer, the 27-year-old Bublik delighted the crowd with an underarm serve but ultimately could do nothing to stop the Italian's march into the last four.
Three-time champion Novak Djokovic kept up his quest for a record-breaking 25th Grand Slam title, battling past third seed Alexander Zverev 4-6 6-3 6-2 6-4 to set up a French Open semi-final against Sinner.
The 38-year-old Serbian notched his 101st victory at Roland Garros, site of his Olympic gold medal victory last year at the Paris Games, after three hours and 17 minutes in a match that saw him battle against the German in a 41-shot rally to save a break point.
Former world No 1 Djokovic is just two matches away from becoming the first player, male or female, to win 25 Grand Slam singles trophies.
BOISSON SPARKLES
Earlier, Boisson became the toast of France after staging the tournament's biggest upset with a 7-6(6) 6-3 win over Andreeva, who had been tipped as a title contender, in an electrifying match that had the home crowd on the edge of their seats.
The 22-year-old had stunned third seed Jessica Pegula in round four, but on Wednesday pulled off another major shock, beating Andreeva, who had not lost a set in the tournament.
"Every tennis player dreams of winning a Slam - and for a French player, Roland Garros even more so. I’ll go for it because my dream is to win the final, not the semi-final,” Boisson said.
Andreeva, the 18-year-old sixth seed who was bidding to become the youngest female player to reach back-to-back French Open semi-finals in nearly three decades, quickly found herself chasing Boisson's fierce forehand.
The underdog, who has been a breath of fresh air in the tournament with her no-nonsense power game and down-to-earth approach, looked to have run out of steam as Andreeva went 3-0 up but she proceeded to win the next six consecutive games.
Andreeva repeatedly lost her temper and was handed a warning when she fired a ball into the stands in frustration.
With the home crowd the loudest it had been since the start, chants of 'Lois, Lois' echoed across the Philippe Chatrier court, with the decibel level lifted even further because the roof was closed due to rain.
Boisson, who will jump almost 300 places in the rankings next week, will face 2023 US Open champion Coco Gauff, who came out on top in an error-ridden quarter-final against Australian Open champion Madison Keys with the pair littering the court with 101 unforced errors.
With a total of 49 unforced errors in the first set alone they both struggled to hold serve and Gauff, a semi-finalist in Paris last year, wasted a set point before Keys, who reached the French Open last four in 2018, edged ahead with a tiebreak win.
Gauff, who reached the final here in 2022 and is the youngest woman to claim 25 main-draw wins at Roland Garros since Martina Hingis (1995-2000), bounced back to win the next two sets.
"So many unforced errors," Gauff, who also had 10 double faults, said to herself after sinking another easy baseline shot into the net.
"I was just trying to be aggressive," the 21-year-old Gauff said. "Usually if you're playing too passive, in the end the more aggressive player is going to win. I knew in the second and the third that I had to try my best."
GAUFF TO FACE BOISSON, SABALENKA AND SWIATEK BLOCKBUSTER
Gauff will be up against not just a plucky Boisson but the partisan French crowd as well, hoping to take a step towards a second major title.
"I've been in crowds where they're 99% for me, so I don't have an issue with it. I hope everyone will be respectful and things. If not, it's cool," Gauff said before the 361st-ranked Boisson stunned sixth seed Andreeva.
"It makes sports exciting and I can't get irritated at the fact that someone's rooting for their hometown hero, because I would do the same. It's something I'll mentally prepare for if it were to happen and expect and be ready for."
Belarusian Ayrna Sabalenka has been the poster girl for Grand Slam consistency in the last few years, storming into the semi-finals in nine of the last 10 majors she has competed in to emerge as a genuine threat to Iga Swiatek's supremacy on Parisian clay.
The 27-year-old top seed's growing composure and mental fortitude on the biggest stage means that the wobbles she once experienced have become distant memories, while her retooled serve and power can blow away opponents on any surface.
She has harnessed all those qualities during her run to the last four without conceding a set, dismantling Olympic champion Zheng Qinwen 7-6(3) 6-3 in the last round.
Swiatek, who is on a 26-match winning run at the French Open, represents the biggest test in Sabalenka's bid to win a maiden Roland Garros title and add more silverware to her trophy cabinet that contains US and Australian Open crowns.
Having locked down the top ranking since April 2022, the duo renew their rivalry having become a little closer after making a TikTok video at last year's season-ending WTA Finals in Riyadh and practising together thereafter.
"Before, there wasn't any communication or any practice with her, but now we're getting better. We get along and we practise more often. We know each other well," Sabalenka said.
"We've had a lot of great battles in the past ... I'm super excited to go out there and to fight and to do everything I need to get the win."
Fifth seed Swiatek leads the overall head-to-head record with Sabalenka at 8-4 but the gulf in class on clay is a little more evident at 5-1 in favour of the 24-year-old.
