"We're happy to see there's an atmosphere, emotions and that the spectators are there. However, we will be uncompromising with respect to the players and the game," said Mauresmo.
"If there's the slightest behaviour that oversteps the mark, it will be the exit," asserted Mauresmo, while acknowledging that "identifying the person is not always easy".
Alcohol will be prohibited in the stands, with both security agents and match umpires instructed to take a much more severe approach towards troublemakers.
Goffin claimed he was spat at by a spectator as he defeated French player Giovanni Mpetshi Perricard in the opening round on Tuesday.
Mauresmo, a former world number one and two-time Grand Slam champion, said there would be "no hesitation" to remove anyone caught throwing something at a player.
She said it would be at an umpire's discretion how to handle other disruptive spectators, but called for them to be sterner.
Swiatek scolded spectators for making noise during points after her tense second-round win over Naomi Osaka.
"There will likely be situations when it comes down to judgement," said Mauresmo.
"Throwing something at a player, you're out. Expressing yourself during a point is a no-no, we're going to try and limit that as much as possible.
"The umpires have tighter, even more precise instructions on keeping the audience under control. It's part of the role of the umpire to manage that too."
