In the September 5, 1956, issue of the Mobile Press-Register, the following notice appeared. "Harold Daniels has been named by the American National Films, newly organized Mobile motion picture producing company, as director of its first film, 'Bitter Swamp.' Production on the film is scheduled to begin Oct. 1 on location in Louisiana."
The Saturday, June 1, 1957, issue of the newspaper had more information about the film. "Big, blonde Peter Graves, star of the Mobilian produced film 'Bayou' stood up in the Admiral Semmes Hotel last night and delivered himself of an address on Hollywood methods...Michael Ripps, Mobile producer of the film, told of some of the difficulties experienced in shooting on the Louisiana location."
So we learn several things from these two brief paragraphs about Bayou, which had its original release in June 1957. American National Films, a Mobile company, produced the picture. According to the IMDB, Bayou was the firm's only movie. As mentioned in the first notice, Harold Daniels did indeed direct the film. In addition to his 19 credits as an actor, Daniels directed 24 feature and TV movies including My World Dies Screaming in 1958 and House of the Black Death in 1964. A native of Buffalo, New York, he died in 1971.
The movie was filmed on location around Barataria Bay in Louisiana. Executive Producer Michael A. Ripps has several other credits in the IMDB. He is listed as writer of The Fat Black Pussycat  and producer of Common Law Wife  among a few other classics. Edward I. Fessler is listed as the author of both the story and screenplay for the film; it's the only credit given for him at the Internet Movie Database. By the time of first release the movie's title had been changed and it would acquire another title on re-release. United Artists distributed Bayou but the film did poorly despite such a major firm's support.
The tag line for initial release, as seen on the poster below, was "Somewhere, a 15-year old girl may be a teenager...in the Cajun country, she's a woman full-grown!...and every Bayou man knows it." So does Martin Davis, a young architect from New York, who comes to New Orleans on business and is taken to a carnival in Cajun country. There he meets Marie, the teenager, who's working to support her father and is lusted after by Ulysses, a brutal local store owner who has attempted to rape her. Read the summary at Wikipedia or find a copy of the film if you can to see how this New York vs. Cajun competition turned out.
Peter Graves played the architect; he would go on to a prominent career on television in Mission Impossible and other programs. The role of Ulysses fell to Tim Carey, a character actor who had appeared in such classics as East of Eden and Paths of Glory. Ed Nelson, who would go on to later fame in the TV series Peyton Place, and Jonathan Haze, largely known for a role in the original Little Shop of Horrors, were also in the cast.
Marie, the cause of it all, was played by Lita Milan, whose acting career was a mix of film and television roles. She is probably best remembered as the female lead in Paul Newman's western, The Left Handed Gun . The Glamour Girls of the Silver Screen web site has much detail about her life and acting. Unfortunately, according to an article from 2013, she was at that time living in poverty in Madrid, Spain.
As noted above, Bayou did not perform well during its first release. In 1961 rights to the film were purchased, and it became Poor White Trash which circulated on the drive-in circuit around the South for years. The film should not be confused with another one of that title released in 2000. I have no idea if the movie is currently available in any format or via streaming. Please enlighten us in the comment section if you have more information!
Source: Rotten Tomatoes
Graves in 1967
Lita Milan on the lobby card for Bayou
I doubt that's the Cajun country of Louisiana behind her, but Ms. Milan probably made good use of this sultry look in Bayou.
Ed Nelson in his role as Dr. Michael Rossi in the TV version of Peyton Place
Jonathan Haze in his most famous role in the 1960 Roger Corman film Little Shop of Horrors