Paire, who was seeded 16th at the Rio Games, was sent home after being kicked off France's team.
The 27-year-old Paire, ranked No. 34 in the world, broke team rules, the FFF said in its statement Sunday. He reportedly sometimes stayed away from the village or came back late. He also made dismissive comments about the importance of the Games because there are no ranking points.
Mladenovic and Garcia "sharply criticized" the FFF following their defeat in the first round of the doubles over a clothing mix-up, saying they were not informed by their federation that, as doubles partners, they had to wear the same colors.
The pair was told just before going on court that it could lose by default if the players did not change their clothing, and Mladenovic had to lend Garcia some spare gear.
Mladenovic was particularly angry, posting five tweets in which she lambasted what she called the "incompetence" of the FFF, blaming it for "ruining" their match.
The FFF said all three showed an "unacceptable attitude," adding that they are provisionally suspended from selection until a final decision is made Sept. 24.
Mladenovic and Garcia are key players in France's Fed Cup team that will contest the final against the Czech Republic in November.
France plays away to Croatia in the Davis Cup semifinals Sept. 16-18, meaning that Paire is ineligible to play. However, he has yet to represent France and was not expected to be selected.
The FFF added that the three will receive no help from the federation during the suspension.