For those wondering about the English, note that we wouldn't say "put on" with a general CD-ROM, only a music CD or a DVD, where music or a video would be "on" as a result of the action (and "put on" also works for a vinyl record, as La_Mariette mentions below).
We'd say "put in" for inserting a CD-ROM with a computer program or files on it, because we're not necessarily turning something on, and we don't really think of a computer program being "on" in any event, even when it's "running".
If the French phrase is applicable to general CD-ROMs as well as to audio and video media, that's a hands-down argument for "put in" to be accepted as an alternative English translation.
"Put on" is okay as a default in any event, because it's the act of starting the music or the video, not just inserting the disc (and it works for a vinyl record as well), though we could still use "put in" to describe the physical act of inserting a music CD or a DVD.
They seem to "(faire) jouer de la musique" and "jouer d'un instrument", but to "mettre un disque":
French native speakers?
No. Your English sentence is in the present tense. The French sentence at hand refers to something that has already happened. The verb is in the passé composé ("a mis"). It translates to either "she put" (simple past) or "she has put" (present perfect), not "she puts".