What's a calming color paint that would go well with a deep violet carpet it's in a well lit room with knotty pine ceiling and borders and lots of plants?

Your room sounds beautiful! My suggestion would be that you choose a beige/taupe with a hint of purple/lavender/violet. Pick a beige/taupe that goes well with your knotty pine. Try to match the warmth of the wood in the paint color.

Another option would be to go with a warm sage gray/green scheme if this is more of a an indoor/outdoor room. This color would really complement the plants.

I'm not sure what you mean by borders. If they are wallpaper borders, consider pulling a color from them to tie the room together.