If it's burgundy solid pine furniture or any burgundy leather furniture, you must have colours that will balance out its' assertive tone. The best choices are the ones closest to the burgundy in accordance to the color wheel. First, you can try green or green-gray walls. If you are not a fan of green, you can use blue or blue-gray walls. Beige or Yellow-Ochre walls are also a good choice along with warm-gray or taupe walls.