Muguruza briefly left the room after starting to cry when asked about Mladenovic's regular outbursts at key points, but the fourth seed later claimed to be unperturbed by her opponent's behaviour.
The 27-year-old Bacsinszky, who had wasted two set points in the first set, frustrated the American by playing a string of drop shots and won the next two sets easily.
But as the match went on Muguruza settled in-as the crowd settled down-and the Spaniard found her groove in the second set to force a decider. "Sometimes", she added, "(fans) should be a little bit more respectful".
Mladenovic raced through the first set but Muguruza pegged her back, with the Spaniard looking much more like the player who stunned Serena Williams past year than the one who has failed to make a single final since. It's thanks to you that I fought for every point. "If you had been in my shoes on the court, I think you would have understood", she told reporters.
The Spaniard clearly did not enjoy the pro-Mladenovic vocal crowd, who were quick to chide her when she ambled to the net to have a glance at a ball mark when one of her backhands sailed just wide of the tramline late in the match.
Williams, whose sister Serena is not playing in the tournament as she is expecting her first child, ran out of steam in the last two sets.
Of the 12 survivors this year, only Romanian Simona Halep has reached a French Open final.
"Yeah, I can say it can be a copy of Stan, because he's a great champion and I respect him a lot".
Tagged one of the pre-tournament favourites after reaching the final in Madrid and Stuttgart, the 13th seed is looking to become the first French woman since Mary Pierce in 2000 to lift the Suzanne Lenglen Cup.
100 - Rafael Nadal contested his 100th best-of-five match on clay on Friday.
- Trump tweets against Germany, escalating row after tense summits
- Sony 'refused' cross platform Minecraft
- Warriors' Green will be on the court for this Finals Game 5
- Trump expects Senate health care bill in summer
- Congressman DeSantis says he's 'lucky' he left baseball practice early
- IPad Pro 10.5 Review: A Surprisingly Powerful Tablet
- May's top aides resign after UK election fiasco
- E3 2017 Ubisoft's Keynote: Everything you need to know
- Puerto Rico upholds statehood demand in contentious vote
- Insomniac's Spider-Man debuts gameplay footage