Canadian Bouchard had called for Sharapova to be banned for life after the five-time Grand Slam champion tested positive for meldonium at last year's Australian Open, referring to the Russian as a "cheater".
Maria Sharapova shrugged off a sluggish opening to progress to the second round of the WTA Internazionali BNL d'Italia with a win over Christina McHale on the eve of learning her French Open fate.
Sharapova was down a break on three different occasions in the first set but eventually made the necessary adjustments and cruised through the second set to improve her lifetime record to 5-0 against McHale.
Sharapova has played Lucic-Baroni once already since making her comeback, defeating the former Melbourne doubles victor in three sets during the first round of the Madrid Open.
Sharapova was not able to acquire enough ranking points to secure an automatic place in qualifying for the tournament in Paris and so was reliant on a wildcard, with FFT president Bernard Giudicelli hinting that the rejection was due to her recent ban.
After being told in her post-match press conference that she will be returning to Wimbledon this summer, Sharapova said:"I don't know how the Wimbledon qualifying works or the rankings".
"The fact that I'm back and playing three weeks in a row now and three events in a row for me is a big deal".
Tournament organizers were criticized for giving a wild card to Sharapova instead of former French Open champion Francesca Schiavone, an Italian.
"I'll focussed on my match, I'm playing tomorrow", Sharapova said; "But nothing is a disappointment after being away from the game for 15 months".
The match began unsteadily, with three breaks of serve in the first 17 minutes, McHale took an early 3-1 lead.
Berdych matched his coach, Goran Ivanisevic, with 599 career victories.
Lucic-Baroni's level dipped thereafter, though, and consecutive double faults from the veteran gave Sharapova an advantage that she retained throughout set two.
Also, Sam Querrey eliminated Lucas Pouille, a semifinalist past year, 7-6 (6), 7-6 (8). She could face top-ranked Angelique Kerber in the third round. The American player hit 3 winners to 16 unforced errors, while Sharapova 10 winners and 16 unforced too.