Petra Kvitova took the opening set on a break and started the second set with another.
But Mladenovic broke back for 3-all and eventually forced the contest to a tiebreaker, which Kvitova captured.
“I had to fight, but I’m glad that I had this (kind of) match. Hopefully, it’s given me a bit more freedom for the next round,” last month’s Stuttgart clay winner said.
Sloane Stephens beat former world number one Victoria Azarenka 6-4, 2-6, 6-2 to equal her best showing at the event, defeating the two-time Australian Open winner for the fourth consecutive time.
Belarusian Azarenka committed nine double-faults in going down to the American eighth seed.
“I was taking control from the baseline points, I was doing the right things,” Azarenka said.
“I was playing smart tennis. But I didn’t create anything with my serve today and it was really frustrating.
“I didn’t really have a game plan, that’s something I need to take a look at and fix.
“I need to make it more simple and just do the right things.”
Former US Open winner Stephens also reached the third round here in 2014 and 2018.
Dutch seventh seed Kiki Bertens advanced past 2017 Roland Garros champion Jelena Ostapenko 6-4, 6-3.
Last year’s losing Madrid finalist Bertens hammered 11 aces as she went through in 80 minutes, breaking Ostapenko four times.
In the men’s first round at the ATP-WTA pre-Roland Garros tune-up, Russian 11th seed Karen Khachanov ended a five-match losing streak as he put out Spain’s Jaume Munar 6-4, 6-7 (5/7), 6-3.
Khachanov earned his last win in mid-March at Indian Wells.
An indifferent season continued for 2017 ATP Finals champion Grigor Dimitrov, with the Bulgarian falling to Taylor Fritz 7-6 (10/8), 7-6 (7/4).
Germany’s Philipp Kohlschreiber defeated Mikhail Kukushkin 6-2, 7-6 (7/5), while Frances Tiafoe beat Georgia’s Nikolaz Basilashvili 6-7 (8/10), 6-3, 6-4.
A French pair advanced in opening matches with Richard Gasquet, playing for the first time since October due to injury, beating Spanish youngster Alejandro Davidovich Fokina, last weekend’s Estoril semi-finalist, 7-5, 7-6 (7/5).
Gael Monfils, the 15th seed, continued an injury comeback, taking out Italy’s Andreas Seppi 6-3, 6-1.
