Burgundy is a challenging colour and can be depressing! I would use a fresh shade of apricot, aqua/duck egg, or pale storm-cloud blue on the walls. Are you in the UK or US?

You can think exotic jewel tones: orange, gold, aubergine, burgundy all work togetherI do love the idea of aqua or duck egg but it has to be done with panache to work well https://www.houzz.com/photos/color-tells-a-story-mediterranean-living-room-detroit-phvw-vp~4905985

could we have a picture? I think if you start by finding a material that you like then you can pick out colours from there. I think a grey/beige would be nice for the walls with some really different cushions. I really like the idea of aubergine and burgandy together. What colour are your carpets?

Also, what is the light quality in the room - is it north facing (cool, low light) or south facing (warm, bright light)? If you search Google Images for, e.g. 'wall colors with burgundy sofa' (and other search term variations) you will see some ideas.