I think that H1954 and MerylStreep make important points here and I'm wondering if it's not quite the time to be making any big changes because you possibly haven't yet a firm plan or a timescale for the alterations you wish to make ?
The cheapest way to make a big change is paint and/or paper. But paint is still an expensive outlay IF you are not sure about the other purchases or eventual colours for furnishings for the room.
I would be happy to hold on to the Hessian colour whilst I made up my mind. If you are going to change the sofas or chairs, change the curtains etc., then maybe re-painting might be a waste of your money and time unless you have the colours fixed in your head now.
Since the room currently sounds as if it may be a bit 'too beige', you could lift that feeling slightly by painting maybe one of the walls in white - not brilliant white and not magnolia but one of the many whites which would look great with the hessian colour. This would help to show off the white poppies better and look quite fresh, maybe. Houseplants and greenery bring a calm and decorative touch, perhaps the fireplace wall could be painted white instead. Adding some bright cushions in a solid colour around the room would also help you make a mark and wouldn't cost a fortune. If you sew, making simple envelope cushion covers takes no time and helps contrast or complement and pull the colours of the room together.
Since choosing completely new paint colours, carpets, furniture, etc., is so difficult - and it'd be awfully expensive to make a mistake - it's often easier to focus on a particular item which is going to feature in the new room - a chair or rug or something with pattern and colour that you like. Choose a couple of colours from there and then find the appropriate tone of paint or paints from a chart or sample pots until you are happy with the effect. It sounds really exciting but I wouldn't rush it until you know exactly what you want to buy.
Good luck!