This is a great song to get you in to the Gypsy Jazz vibe.
These chords are demonstrating the flexibility and artistic license we employ when playing in these songs, and Jazz in general.
- The Gm is really Gm6 without a 5th note
- The A7 is A7 without a 5th note
- The D7 is without a root note!!
- The Ab is really Ab6 without a 5th note
These chord voicing's can be interpreted as other chord names, too.
The power is being able to use these shapes in as many ways as possible
I have written out a way to play the melody including the finger choices.
You can play it elsewhere if you like.
Just remember, play it all with Downstrokes where possible.