The Russian former world number one was told on Tuesday that despite serving her 15-month ban for doping she would have to miss the second Grand Slam of the season.
Announcing the decision, FFT president Bernard Guidicelli said he was sorry for Sharapova but added "it is my responsibility and my mission to respect the high standards of the game to be played without any doping."
WTA chief executive Steve Simon took issue with the FFT's hard line stance on the two-time French Open champion in a strongly worded statement.
"She has complied with the sanction imposed by CAS (the Court of Arbitration for Sport).
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"The tennis anti-doping program (TADP) is a uniform effort supported by the Grand Slams, WTA, ITF and ATP.
"There are no grounds for any member of the TADP to penalise any player beyond the sanctions set forth in the final decisions resolving these matters."
The five-time Grand Slam champion was banned for two years for using meldonium, with the penalty later reduced by CAS which ruled she was not an intentional doper.
She is guaranteed a qualifying spot at Wimbledon in July after winning her opening match at the ongoing Rome Masters, although she missed a chance at direct entrance into the main draw after a second-round exit on Tuesday.
Sharapova, whose ranking has plummeted to 211, could have earned her spot at Wimbledon by reaching the semi-finals in Italy but retired from her match against Mirjana Lucic-Baroni in the final set with a thigh injury.
The 2012 and 2014 French Open winner has yet to publically comment on her Roland Garros snub which was delivered by Guidicelli on Facebook Live, ahead of the May 28 -June 11 tournament.
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"Nobody can deprive her of her two titles at Roland Garros, but today I can't grant her the wildcard requested," he said.
"The titles won here, she won within the rules without owing anything to anyone.
"I know the media dimension of Maria and I'm measuring the expectations of the public and sponsors, but in all conscience it didn't appear possible to me to go beyond the strict application of the world anti-doping code."
French Open tournament director Guy Forget had earlier Tuesday said the decision over whether Sharapova would receive a wild card was going to be "very controversial".
"As you talk with players, it's very controversial. So no matter what happens, there will be a lot of questions around that wildcard," Forget told the BBC.
"I don't think that's right. She's a cheater and so to me, I don't think a cheater in any sport should be allowed to play that sport again," Bouchard, the world number 52, told TRT World while playing at the Istanbul Cup.
Sharapova's absence leaves the women's French Open field wide open with Serena Williams, a three-time champion in Paris, sitting out the rest of the season as she prepares to give birth to her first child.