Azarenka, seeded 15th, had only 13 unforced errors to Andrea Petkovic's 42 in a 6-1, 7-6 (3) win.
Raducanu, 19, lost to Aliaksandra Sasnovich of Belarus 3-6, 6-1, 6-1 to end her tournament debut after failing to convert on five break-point chances at 1-1 in the third set.
Raducanu's loss means all four reigning Grand Slam champions have been eliminated by the second round -- the first time that has happened since the 2014 French Open, according to the WTA. 2021 French Open champion Barbora Krejcikova was knocked out in the first round, and reigning Wimbledon and Australian Open champion Ash Barty retired in March.
Azarenka has twice won the Australian Open and was a semifinalist at Roland Garros in 2013.
Petkovic, 34, reached the French Open semifinals in 2014 but has not been beyond the third round at any Grand Slam since then. She is a five-time clay-court champion on the tour.
Sasnovich won 12 of 14 service points in the second set en route to her 16th career victory over a top-20 player. She advanced to the third round at Roland Garros for the first time in her seventh appearance.
The 28-year-old Sasnovich had also beaten Raducanu at Indian Wells last year in the British player's first match after winning the title at Flushing Meadows.
The Associated Press contributed to this report.