The song was originally written for a love interest for Philip Baptiste. It reached number one on the U.S. Billboard R&B chart and number. 2 on the Billboard Hot 100 in 1959.
Cat Power recorded it in 2000 on her album The Covers Record. The 2007 film Juno featured her version in its soundtrack.
The song shares a title with, and features prominently in the plot-line of, the 1989 Harold Becker film Sea of Love starring Al Pacino and Ellen Barkin (Wikipedia)
The link to the original above, is to the Cat Power version that Grace was inspired by. You can find a link to Phil Philips' original version form 1959, in the Reviews, reactions etc. box