This is arguably just a matter of personal preference ... but I would spell it Madame Butterfly.
The composer being Italian, and the libretto being in Italian, the correct spelling would arguably be Madama Butterfly. But the opera was based on a short story by the American lawyer John Luther Long, and he gave it the title Madame Butterfly (spelt the French way).
Long's story was based on the recollections of his sister, Jennie Correll, who had been to Japan with her husband, a Methodist missionary. It also bears many similarities to Madame Chrysanthème, a semi–autobiographical novel by the French naval officer Pierre Loti, which also was set in Nagasaki and was adapted into an opera. It was published in Century magazine in 1898, together with some of Long's other short fiction.
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