Frances Scott Fitzgerald Lanahan Smith, 64, the only child of author F. Scott Fitzgerald and herself a writer for newspapers and magazines, including The Washington Post and The New Yorker, died yesterday at her home in Montgomery, Ala. She had cancer.

Mrs. Smith, whose nickname was Scottie, lived in Washington for several years and was a figure in society here. For the past 13 years she had lived in Montgomery, the hometown of her mother, the former Zelda Sayre. She was born in St. Paul, in her father's home state of Minnesota.

She grew up in Paris when her father was one of the most popular American writers alive and both of her parents symbolized the carefree life style of the Jazz Age. But by the time the family returned to this country, Zelda Fitzgerald already was slipping into the mental instability from which she never recovered. In the mid-1930s, F. Scott Fitzgerald himself had a nervous breakdown.

Mrs. Smith attended the Ethel Walker School in Connecticut and graduated from Vassar College.

Her father, whose novels included "This Side of Paradise," "The Great Gatsby," "Tender is the Night" and "The Last Tycoon," died in Hollywood in 1940. Zelda Fitzgerald, a painter and writer who published a book, "Save Me The Waltz," died in a sanitarium fire in North Carolina in 1948.

In her own career, Mrs. Smith worked on the New Yorker's "Talk of the Town" column from 1944 to 1948. She moved to the Washington area in 1950 and was a writer for the Democratic Digest, a publication of the Democratic Party Central Committee. She was a reporter for the Northern Virginia Sun before joining The Post in the early 1960s.

At this newspaper she covered the Washington social scene and wrote a series on Peace Corps operations in Africa. In the mid-1960s, she did a twice-weekly column for The New York Times on Washington society. She was the author of two books and in 1974 was the co-author of "The Romantic Egoists," a journal of photographs of her parents and clippings about their lives.

Mrs. Smith said in a recent interview that being the daughter of a celebrated author opened many doors for her but that it also had its drawbacks. "I've always said jokingly that it was the best-paid part-time job in the world," she said. "It has been hard work sometimes because it encompassed the whole period when my father got extremely popular."

Despite the stories of her parent's seemingly endless partying, she said, "They were always very circumspect around me. I was very unaware of all this drinking that was going on . . . . I was very well taken care of, and I was never neglected. I don't consider I had a very difficult childhood at all. In fact, I consider it a rather wonderful childhood."

Her marriages to Samuel J. Lanahan and C. Grove Smith ended in divorce.

Survivors include three children by her first marriage, Eleanor Lanahan Hazard of Burlington, Vt., Samuel Jackson Lanahan of Eugene, Ore., and Cecelia Scott Ross of Avondale, Pa., and five grandchildren.