Djokovic was first up on Court Suzanne Lenglen, and he was barely troubled by Blaz Kavcic, winning 6-0, 6-4, 6-4 for his 23rd straight Grand Slam victory.
In the main stadium at Roland Garros, Azarenka defeated Dinah Pfizenmaier of Germany 6-1, 6-1, two days after struggling to win her opening match.
It was Federer that ended Djokovic's 43-match winning streak last year, beating the Serb in the semifinals at Roland Garros. If Djokovic wins the French Open title this year, it will be his fourth straight Grand Slam title, and his first at Roland Garros.
Djokovic was broken once by Kavcic, but otherwise had little trouble. He did, however, finish the match with 34 unforced errors, almost twice as many as Kavcic's 21.
Azarenka, who took over the No. 1 ranking after winning the Australian Open, easily advanced against Pfizenmaier on Court Philippe Chatrier.
In the first round, Azarenka struggled early before winning 12 of the final 14 games to win. She committed 60 unforced errors in that opening match, but brought that number down to only 11 on Wednesday.
Azarenka reached the quarterfinals at Roland Garros last year, matching her best performance at the clay-court Grand Slam.
U.S. Open champion Sam Stosur also advanced, beating Irina Falconi of the United States 6-1, 6-4.
On Tuesday, Serena Williams showed that, even after 13 Grand Slam championships and dozens of other titles, she is capable of throwing away a big lead.
Williams led 5-1 in the second-set tiebreaker and was two points from victory nine times but still lost to Virginie Razzano of France 4-6, 7-6 (5), 6-3 - the first time she has ever lost in the first round of a Grand Slam tournament.
''I definitely was nervous. I'm always a little nervous in every match I play, which I think is a little bit healthy,'' said the fifth-seeded Williams, who had been 46-0 in the first round of majors. ''I was definitely a little nervous.''
Williams entered the tournament with a 17-0 record on clay this year. And it looked like No. 18 was in the bag late in the second set.
But Razzano won six straight points to take the set and then won five straight games in the third.
''I just felt I couldn't get a ball in play,'' Williams said. ''You know, when I did, I just felt like I was hitting late and, I mean, how can you hit late on a clay court? It was kind of odd.''
Defending men's champion Rafael Nadal had no such trouble, starting his quest for a record seventh French Open title by beating Simone Bolelli of Italy 6-2, 6-2, 6-1. Maria Sharapova had an even easier time, scoring a ''double bagel'' in her 6-0, 6-0 win over Alexandra Cadantu of Romania.
''I feel like with every year I have improved,'' Sharapova said, ''and I enjoy it much more.''
- Novak Djokovic
- Venus Williams
- Victoria Azarenka
- Serena Williams
- Roland Garros