Hudson portrays the late music icon in the clip as she struggles to find a hit song after releasing four albums.
The singer then starts to find her voice and starts working on one of her most recognizable songs, "Respect."
The trailer also briefly explores Franklin's childhood and marriage to Ted White, portrayed by Marlon Wayans.
Respect, from director Lisel Tommy, is coming to theaters on Aug. 13.
Hudson also discussed the film during a sit-down interview on GMA. Hudson said she was chosen by Franklin to portray her in a movie following her role in 2006's Dreamgirls.
"For her to choose me, I can't even begin to put it into words. I do not take it lightly and I just think it's a dream come true. I don't want to sound cheesy but it is," Hudson said.
Hudson also named "All the Kin's Horses," "Oh Me, Oh My (I'm a Fool for You Baby)," and "Ain't No Way" as her favorite Franklin songs.