After much research, it is apparent to me that Ms. Streisand was the first singer to record "Free Again". The tune was first performed (repeat - performed, not recorded) at the Rose d'Or talent contest in 1965 by Jacqueline Danno. The tune was originally written by Jo Basile, the pseudonym of Joss Baselli, accordionist and veteran of the French music scene in the 1950s and 1960s. Throughout the 1960s, Baselli also worked as a songwriter, and his best-known tune, "Free Again" (French title is "Non C'Est Rien"), was recorded by numerous Anglophone singers - most notably, Barbra Streisand, on her 1966 album, "My Name is Barbra". I suspect that whatever version you are searching for has maybe a retro sound and that's why you think it is from another era. I have provided the link to the Baselli web site as confirmation that the song was written in the 1960s. It could not have been recorded in 1957. Good luck with your continued search.
http://www.spaceagepop.com/basile.htm