World No.40 Mladenovic dominated Tomljanovic on the hard outdoor court to record a 6-1, 6-1 victory in 72 minutes as France took a 1-0 lead at Perth Arena.
Earlier on Saturday, Fed Cup debutant Ajla Tomljanovic was outclassed by France's Kristina Mladenovic 6-1 6-1 in the opening singles rubber.
But if that result left Barty feeling the heat, it didn't show.
Australia's hopes of winning the Fed Cup for the first time in 45 years will rest largely on Barty's shoulders after she had embarrassed former world No.4 Garcia.
"I think that's probably the best tennis match I've ever played in my life and what a place to do it, this is incredible".
"I'm so happy to be back here in Perth".
"Whether we're 1-0 up or 1-0 down, it's still about me doing what I need to do to prepare in a way that gives myself the best chance of winning which, in turn, helps the team".
France last won the Fed Cup in 2003 and most recently made the final in 2016. With no rhythm, Garcia sprayed a forehand mistake in the fourth game to give serve away, wasting those two break chances in game five and netting a forehand in the next game to suffer a awful loss that should provide a massive boost to Barty ahead of deciding Sunday's rubbers.
The ease of her win was a huge relief for Australian captain Alicia Molik, whose gamble to play Tomljanovic in singles ahead of veteran Samantha Stosur spectacularly backfired.
Representing Australia for the first time, Tomljanovic was overcome by nerves and was no match for a red-hot Mladenovic.
"There's not many tournaments throughout the year where you get a second bite of the cherry the day after - what a brilliant situation to be in", Molik said. That's normal for your first match.
With the temperature climbing to 36 degrees before midday and a near-capacity crowd at RAC Arena rallying behind her, the conditions were in world No.51 Tomljanovic's favour.
Fresh from partnering Hungary's Timea Babos to take out the doubles title at last week's season-ending WTA Finals in Shenzhen, China, Mladenovic is set to pose a stern test for Barty. "I nearly played a flawless match".
She was blown off the court by Kristina Mladenovic, who produced 16 winners to the Aussie's two, in a dominant 6-1 6-1 display. "I love these sort of matches, the bigger the pressure, the more special the event". Alicia Molik went with Tomljanovic who couldn't endure the pressure, serving at 42% and barely hitting any victor alongside more than 30 errors! Carried by this momentum, Kristina claimed 13 of the first 14 points in set number two, breaking at love in game two with a forehand return victor and securing the break following a forehand error from Tomljanovic a few minutes later.