The California native is best known for her portrayal of Ann Romano, the single mother of two teen daughters, on the TV sitcom "One Day at a Time," which ran from 1975-84.
The actress announced last September that she had pancreatic cancer.
The Los Angeles Times confirmed her death Friday.
Franklin appeared on her former TV daughter Valerie Bertinelli's new sitcom, "Hot in Cleveland," in 2011 and was a guest star on the soap opera "The Young and the Restless" last year.
She is survived by her mother, Claire Franklin; and stepchildren Jed Minoff and Julie Minoff, the Times said.
Her husband, television and film producer Marvin Minoff, whom she married in 1980, died in 2009.
"My heart is breaking. Bonnie has always been one of the most important women in my life and was a second mother to me," Bertinelli said in a statement to People.com Friday.
"The years on 'One Day at a Time' were some of the happiest of my life, and along with Pat [Harrington Jr.] and Mackenzie [Phillips] we were a family in every way," Bertinelli said. "She taught me how to navigate this business and life itself with grace and humor, and to always be true to yourself. I will miss her terribly."