The music in the film, as I understand it, is an old Spanish tune, brought to the Americas, and played by the 19th c. Californios; "El Sombrero Blanco," (posts of Q, 28 Jun 05) and Escamillo (13 Sept 05), collected by Charles Lummis in 1904.
It is listed by The Folk Dance Federation of California, Inc., as early Californian.

It also is extant in Argentina, according to the website I linked, but I have no knowledge of the Argentine music or how similar it might be.

Singingwolf, do you have the lyrics to the Argentine "El Sombrero Blanco"?