Finding the Production
Here is a digital copy of the program that théâtrophone subscribers would have received on a bi-weekly basis. The productions from the Opéra are listed on the fourth page, which includes the transmission of La Valkyrie at 8 pm on Monday the 14th of November 1904.
With the date and time for the théâtrophone transmission in hand, one can easily find out at least the most important of the cast members. On this page of Le Figaro, a national daily newspaper that began in the early to mid-1800s, we can see a section on the current performances at several venues around the city, including, first and foremost, the Opéra. At the top only the time is given; however, midway down the column, we can read:
"A l'Opéra. La Valkyrie sera chantée ce soir par Mmes Lucienne Bréval, Hatto, Héglon, MM. Rousselière, Delmas, Chambon, etc., etc."
Which translates to:
"At the Opéra. The Valkyrie will be sung tonight by Madames Lucienne Bréval, Hatto, Héglon, Monsieurs Rousselière, Delmas, Chambon, etc., etc."
And thus the cast is known to be the following:
Lucienne Bréval (Brünnhilde)
Jeanne Hatto (Sieglinde)
Meyriane Héglon (Waltraute)
Charles Rousselière (Sigmund)
Marius Chambon (Hunding)
Jean-François Delmas (Wotan)