I know why it has a TV show feel to it: you've chosen a classic progression (I vi IV V) and the beginning of your melody sounds a lot like "Thinking music" from Jeopardy.
Apart from this detail, the melody is a pleasure to listen to. It's true that it sounds more like easy listening than jazz.
Yet with the accordion, you've given it a jazz vibe with chromaticisms and appoggiaturas (at 1'32", for example). If you'd used more, it would have added jazz.
And I thought you were going to go solo at 1'48". You put in a rising chromatic again. I'd have loved it if you'd developed it.
Still, the music is pretty. You've done enough variation on the arrangement to keep it fresh.
It's good music, with melodies that complement each other according to the instruments, but it lacks the jazz touch that would make it fit the theme.