Sharapova, 30, recently returned from a 15-month doping ban after admitting she had used the banned hormone and metabolic modulator meldonium
Bernard Giudicelli, president of the French Tennis Federation, said via a Facebook Live broadcast: "If there can be a wildcard for return from injuries then there cannot be a wildcard for return of doping.
"I'm very sorry for Maria, very sorry for her fans," said Giudicelli.
"They might be very disappointed, she might be very disappointed ... but it's my mission to protect the game and to protect the high standards of (the) game played without any doubts on the result."
Sharapova tweeted Wednesday that "no words, games or actions will ever stop me from reaching my own dreams. And I have many."
The French Tennis Federation's decision also draw a furious response from the head of the Women's Tennis Association (WTA) Steve Simon.
"I do not agree with is the basis put forward by the French Tennis Federation for their decision with respect to Maria Sharapova," said WTA CEO Simon. "She has complied with the sanction imposed by CAS.
"The tennis anti-doping program is a uniform effort supported by the Grand Slams, WTA, ITF, and ATP.
"There are no grounds for any member of the Tennis Anti-Doping Programme to penalize any player beyond the sanctions set forth in the final decisions resolving these matters."
The former world number one returned to tennis last month -- Sharapova reached the Stuttgart Open semifinals -- but the only way she could have got into the French Open, which starts on May 28, was through a wildcard.
The French Tennis Federation wasn't even willing to her give a wildcard into French Open qualifying, which would have almost guaranteed that Sharapova would have reached the main draw.
Sharapova is currently ranked No. 211 in the Women's Tennis Association (WTA) world rankings.
Asked Monday whether she would be disappointed not to receive a wildcard to the second grand slam of the year, Sharapova told reporters: "Nothing is a disappointment after being away from the game for 15 months."
'She is a cheater'
Melodium was only banned at the beginning of 2016 but Sharapova said she had been taking it for over 10 years as she was magnesium deficient and had recorded several irregular electrocardiography (EKG) tests.
The five-time grand slam champion said that her team did not check the updated banned substance list and hence she tested positive for the drug at the 2016 Australian Open.
Sharapova's return has not been well received by many of her fellow professionals.
Kristina Mladenovic said before the pair's meeting in April
that "all the other players are saying she (Sharapova) is a cheater," in comments carried by The Guardian. The French star added: "She's been taking this drug for 10 years and it's a serious drug."
Canada's Eugenie Bouchard also described the Russian as a "cheater" prior to their matchup at the recent Madrid Open
Bouchard said she had "a lot of players coming up to me privately, wishing me good luck," without naming who those players were.
"I got a lot of texts from people in the tennis world that were just rooting for me. I wanted to do it for myself, but also for all these people," she added.
Sharapova received wildcard entry to the Rome Masters this week, where a first round win over Christina McHale ensured she will make the qualifying rounds for Wimbledon next month.
As things stand, a run to the semis in the Italian Capital would guarantee her position in the main draw at the All England Club.
Sharapova is one of the most marketable stars in tennis and the former World No.1 was estimated to be worth up to $195 million
back in 2016.
The French Open draw was already missing one of its biggest stars as the pregnant Serena Williams takes time out before the birth of her first child.
Sharapova was initially banned for two years but this was reduced to 15 months on appeal by the Court of Arbitration for Sport (CAS) which stated she bore no "significant fault" and did not intend to cheat.
Meldonium "demonstrates an increase in endurance performance of athletes, improved rehabilitation after exercise, protection against stress, and enhanced activations of central nervous system functions," according to a 2015 study
in the journal Drug Testing and Analysis.