Is the mural really that brown looking or is it more like this? If more like this, you have some gorgeous greens, blues and grays to pull out of the picture for color that will work beautifully with the warmer colors of the mural.

I'll get this started, hopefully others see it with some great suggestions. :)

Green. Sage, celedon, forest. There's also a splotch of what looks like grey-blue at the top near the center so I think you could pull off a medium neutral grey. Or white walls would work. White Dove has grey undertones and is a nice go-to.

Of course the paint colour will be driven by the other features of the room too: lighting, furniture, floor, wood tones... Really, art can be completely ignored when you're choosing paint, if the art is a beloved piece such as this one. It will fit no matter what because it is authentically You.

ETA: oops, cpartist got it started while I typed. Neat to see we had the same ideas :)