Fíne is a Gaelic-Irish feminine given name.

At least two women named Fín or Fíne are attested in the Irish annals:

Fín, princess of Cenél nEógain, wife of Oswiu of Northumbria (d. 670). Fíne, abatissa or banabb of Kildare.

References

http://medievalscotland.org/kmo/AnnalsIndex/Feminine/Fine.shtml