This song is about Eleanor Friedberger, the vocalist of the indie rock duo The Fiery Furnaces, who supported Franz Ferdinand during their 2004 tour. Eleanor Friedberger has a relationship with the lead singer of Franz Ferdinand Alex Kapranos.
Because of the Beatlesque feel to the song, especially the album version, the "Eleanor" in the title may also be a reference to "Eleanor Rigby."
A new, updated version was released as a single peaking at #30 in the UK.
Suggestion credit: Edward Pearce - Ashford, Kent, England, for all above
Alex Kapranos claimed that there were a lot of songs about a girl named Eleanor ("Eleanor Rigby" by The Beatles, "Eleanor" by The Gathering and The Turtles), so they wanted to contribute with their own Eleanor song.
Suggestion credit: Lexico - Buenos Aires, Argentina
Eleanor Friedberger also dated Spoon frontman Britt Daniel; Spoon's 2001 song "Anything You Want" is about her.