Ranked 10 places lower than Mladenovic at 40th in the world, Garcia was more consistent than the French number one, who started well but paid dearly for two slow starts to the second and third sets.
Mladenovic also struggled with her first serve, sending over just 30 percent of them in the last two sets and Garcia took full advantage of her opponent's poor second serve.
The second of the day's singles later opposed Caroline Garcia and former French Open finalist Sara Errani.
Italy won the last of their four Fed Cups in 2013. France has won the cup twice in 1997 and 2003.