The actor's outfit drew direct inspiration from Christian Dior's New Look of 1947, a collection credited with revolutionising women's fashion in the 1940s.
Fanning's look, which she wore for the premiere of Quentin Tarantino's latest film Once Upon a Time In Hollywood, featured an ivory, silk organza shirt; a night-blue tulle skirt designed by Dior creative director Maria Grazia Chiuri; and a black, wide-brimmed hat placed in a slanting position.
Many of Fanning's fans have showered the actor with praise on Twitter for her elegant take on old Hollywood glamour.
"Just a note to say Elle Fanning is out there being totally iconic at Cannes," one person tweeted.
"First she passes out at a Chopard dinner because her 1950s Prada prom dress was corseted too tight, then she shows up on the red carpet like this."
"Elle Fanning in Christian Dior is divinity," another added.
Three months after the establishment of the House of Dior in December 1946, Christian Dior launched his first spring/summer fashion collection for the designer brand.
While the fashion designer's combination of a wide, mid-length skirt, tightly-fitted, button-up jacket and hat was perceived as highly glamorous by some, others were none-too-pleased with the design.
Dior received criticism from fellow designer Coco Chanel, who described his vision as being "uncomfortable" for women.
During a protest against the New Look in Chicago, banners were held adorned with slogans such as: "We abhor dresses to the floor! Women, join the fight for freedom in the manner of dress!"
Nonetheless, several people have expressed their admiration for Fanning's tribute to Dior's classic design.
"I can't get over this look! Elle Fanning's homage to Dior's 'New Look' from 1947 is literally everything. So effortlessly chic!" one person tweeted.
On Monday evening, the actor fainted while attending a Chopard Trophy dinner at Cannes Film Festival.
Fanning posted a selfie on Instagram following the incident, with the caption: “Oops, had a fainting spell tonight in my 1950s Prada prom dress but it’s all good!! #dresstootight #timeofthemonth."
"Jesus Christ, reading about Elle Fanning, a *very* thin actress FAINTING because her sample size Prada dress was too tight, and then blaming it on her period, rather than the fact that sample sizes are f***ing INSANE these days... is symptomatic of a huge problem in fashion..." Jamil tweeted.
"Incredibly slender Elle shouldn’t be blaming herself for being a few pounds heavier on her period. She should be horrified at the size of the dress."
Jamil added that she is not "hitting out" at Fanning, but at the pressures of the fashion industry.
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