I was unable to find an album that this song is from but I believe the artist and song title are correct. This clip is taken from Samurai Champloo Episode 20 (Elegy of Entrapment).
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The piece Sara sings and refers to is called "Kuzunoha no kowakare" ("Kuzunoha's Child Separation"), a very long song/recitation created by the famous performer Matsuzaka Saimon.
Kuzunoha was a kitsune, a fox who took human form, and in the guise of a maiden (in some versions a princess), married Abe no Yasuna, a twelfth-century nobleman who had saved the fox from hunters. Kuzunoha bore him a child, who would become the future famous astrologer and onmyouji Abe no Seimei. Ultimately Kuzunoha was compelled by various circumstances (depending on the version of the dramatization or legend) to reclaim her fox nature and return to her natural home in Shinoda Forest. So with unbearable sadness she abandoned her husband and son, after writing a famous farewell poem on which the song is based. The poem may be read as:"Koishiku ba / tazunekite miyo / izumi naru / shinoda no mori no / urami kuzunoha" ("If you long to love me, / Search for me in / Shinoda Forest, Izumi Province / with regret, Kuzunoha.").
There is also a pun between her name 'Kuzunoha' and 'kudzu no ha', the "kuzu leaf" (arrowroot) that grows in the Shinoda forest, which is referenced by Anime-Forever in their sub of the episode.
--The recording used in the series is sung by Tsukioka Yukiko, who studied the recordings of the "last of the Goze'", Haru Kobayashi and Shizu Sugimoto, and even traveled a pilgrimage of all 88 temples of Shikoku island to understand the harsh life of the traveling performers.
