The original Frogger the music on that one was from some childrens tv show in Japan one of if not its theme song. I saw that some months ago and watched the clip and it's right in there a few times as part of a verse.
Inu No Omawarisan
The original Frogger used music from multiple sources, including opening title themes from four then-recent anime TV series, as I noted in this post last year. In that post, I also noted the game's use of "a traditional Japanese children's song," by which I meant "Inu no Omawarisan" ("The Doggy Policeman"). At the time, I was under the impression that it was a very old song, old enough to be in the public domain, but I discovered a few months ago from the song's Wikipedia page that it was written and first broadcast in the early 1960s. Thus, it is still under copyright protection and would need to be licensed in order for the Parker Brothers Frogger to ever be commercially made available again; that song is one of the port's two pieces of music.
This is my 799th post.