Bouchard, dubbed the next big thing of women's tennis last year, arrived in Paris having lost six of her last seven matches and there was no improvement on court Suzanne Lenglen.
Caroline Wozniacki pulls out of Roland Garros
The Wimbledon runner-up, who had reached the last four at Roland Garros last year, resisted in the opening set but was completely overwhelmed in the second.
Mladenovic, ranked 44th in the world, struggled to handle the pressure after opening a 5-0 lead in the second set but a strong first serve on match point ensured a second-round meeting with Czech Klara Koukalova or Montenegro's Danka Kovinic.
"I expected a good season, better than last year," Bouchard told a news conference. "I have learned a lot recently. Moreover I have to be patient.
"The results won't come immediately. I know I can go through difficult times.
"When I'm playing my best tennis is when I'm being more instinctive. I think that's something I need to get back... trusting myself because I know I can play well."
Bouchard has failed to win more than two matches in a row since reaching the Australian Open quarter-finals at the start of the year.
Last term she reached the last four in three of the Grand Slams.
The 21-year-old Bouchard now plans to compete in a couple of warm-up tournaments before heading back to Wimbledon.
Results from the French Open Women's Singles Round 1 matches on Tuesday
Belinda Bencic (Switzerland) beat Daniela Hantuchova (Slovakia) 6-3 6-3
Danka Kovinic (Montenegro) beat Klara Koukalova (Czech Republic) 6-3 7-6(4)
Anna-Lena Friedsam (Germany) beat Alexa Glatch (U.S.) 6-2 4-6 6-4
1-Serena Williams (U.S.) beat Andrea Hlavackova (Czech Republic) 6-2 6-3
16-Madison Keys (U.S.) beat Varvara Lepchenko (U.S.) 7-6(3) 6-3
Irina Falconi (U.S.) beat Manon Arcangioli (France) 6-2 6-0
Kristina Mladenovic (France) beat 6-Eugenie Bouchard (Canada) 6-4 6-4
Francesca Schiavone (Italy) beat Wang Qiang (China) 3-6 6-3 6-4
Sesil Karatantcheva (Bulgaria) beat 25-Jelena Jankovic (Serbia) 6-3 6-4
10-Andrea Petkovic (Germany) beat Shelby Rogers (U.S.) 6-2 6-1
Alison Van Uytvanck (Belgium) beat Anna Karolina Schmiedlova (Slovakia) 7-6(4) 7-6(7)
23-Timea Bacsinszky (Switzerland) beat Lara Arruabarrena Vecino (Spain) 6-3 6-4
Silvia Soler Espinosa (Spain) beat Pauline Parmentier (France) 6-4 6-3
5-Caroline Wozniacki (Denmark) beat Karin Knapp (Italy) 6-3 6-0
32-Zarina Diyas (Kazakhstan) beat Dinah Pfizenmaier (Germany) 6-4 6-1
4-Petra Kvitova (Czech Republic) beat Marina Erakovic (New Zealand) 6-4 3-6 6-4
Julia Goerges (Germany) beat CoCo Vandeweghe (U.S.) 6-2 5-7 6-1
18-Svetlana Kuznetsova (Russia) beat Kiki Bertens (Netherlands) 6-1 4-6 6-2
Tereza Smitkova (Czech Republic) beat Taylor Townsend (U.S.) 6-3 6-4
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