Franklyn Mansfield Branley was born in New Rochelle, New York, the child of an insurance salesman and his wife. While he was still a toddler, Branley's mother died of influenza, and he and his two brothers went to live with a farm family near Newburgh, New York. His father visited them on the weekends. Branley contracted polio at a young age.

After graduating from the New Paltz Normal School (now SUNY), he married Margaret Lemon, who became a grade school teacher. He became a science teacher educator at the New Jersey State Teachers College. In 1956, he joined the American Museum-Hayden Planetarium to run the Planetariums education program. While working there, he also earned a Masters degree from New York University, followed by an Ed.D. from Columbia Teachers College. In 1968, he became the chairman of the Hayden Planetarium, where he served until his retirement in 1972.

Over the course of his career, Branley was a prolific writer, specializing in books that make science accessible to grade-school children. He wrote over 200 books.