Eighth-seeded Raonic, from Thornhill, Ont., dispatched Spain's Marcel Granollers 6-3, 6-3, 6-3, while Bouchard cruised past Germany's Angelique Kerber 6-1, 6-2.
"I'm not surprised to make by first Grand Slam quarter-final but I would not have thought I would have done it first here on clay," said Raonic. "I've always felt I could play well on clay.
"The key is not making much of a change in my game just for the clay. I've been trying to keep what I've been doing on the hardcourts.
Raonic will be the first Canadian man to play a Grand Slam quarter-final since Mike Belkin at the 1968 Australia Championships, which was renamed the Australian Open the following year. He is also the fourth Canadian man in history to reach the last eight at a major: Robert Powell (1908, 1910 and 1912 Wimbledon), William Johnston (1922-23 US Championships) and Belkin.
Bouchard is the first Canadian woman to make the quarter-finals in Paris since Helen Kelesi did it in 1989.
Raonic fired only six aces but went up an early break in each of the three sets in a contest which lasted less than two hours.
"It's been working out well for me," said Raonic. "If I can put this level of tennis together I believe that I have it in myself (to win a Grand Slam title)."
Raonic will face Serbian second seed Novak Djokovic, a winner over France's Jo-Wilfried Tsonga 6-1, 6-4, 6-1. Djokovic beat Raonic in a Rome semifinal last month.
"I'm happy about this win, there are a lot of good things that can come from it," said Raonic. "I'm happy with my level and it's showing in my results. It's also due to all the work I've been putting in."
Earlier, Bouchard needed just 52 minutes to defeat Kerber. She'll face Spain's Carla Suarez Navarro in the quarter-finals of the women's tournament.
"I'm confident and I really believe in my skills. I believe I can play with the best girls out there," said Bouchard. "She's top 10, so I respect her. She can play some really good tennis. I was really mentally prepared for anything, for a battle.
"That mindset kind of helped me, it made me realize whatever happens I can deal with it on the court. I was really going for my shots. That was my intention and it worked."
Bouchard stormed to her victory with 30 winners and 11 unforced errors. She broke Kerber on four of seven occasions as she took revenge for a US Open second-round loss to the German last year.
Bouchard never wavered as she dominated Kerber to win her ninth straight match, the longest win streak of her career. She snapped up the opening set in 22 minutes and was equally lethal in the second as Kerber failed on the only break point she had during the match.
"I just felt good out there, I executed my game plan really well, so I'm happy with that," said Bouchard. "There are always things to improve, and I'm just going to focus on that tomorrow and try to do even better my next match."
Victory lifted her career record against top 10 opponents to 5-10. Her victims this season included No. 10 Sara Errani at Indian Wells in March and No. 8 Jelena Jankovic last April in Charleston.
Bouchard has a 13-4 record at Grand Slams and is 29-11 on the season.
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