Bring in an expert on windows like these. Not only style but material type is going to be important when there is sun exposure.
There are lots of options. Hours probably has a section on window treatments for cathedral windows. There are many wonderful books and magazines devoted to window treatments too. Home Depot has a good selection.

Do you want the top sections exposed or covered? Do you want a contemporary look, soft look and do you want to keep sun out or privacy?

The best option (in my opinion) for shaped windows like that are plantation shutters.

Thank you so much for your comments. I'd like the top sections to be covered at certain times of the day to keep the sun out, but use a blind that I could lift open to expose as much of the window as possible at other times.
I was thinking of draping a light chiffon type material somewhere around them to soften the look. It's a 25m2 room so I'm trying to add as much soft material as possible.

Lucidos I love the idea of motorised sunshades, I think i'll look into this. For a soft look I was thinking of draping chiffon down the sides.

Luscious, do you have a source for these types of shades?

It all depends on where you live...Most local blind places can source these..and not something you can really hang yourself - Hunter Douglas and even Home Depot can work with you on these.

Jean - Consider a Belgium Linen. Almost as soft as chiffon but a bit more weight then the chiffon and a wonderful texture. They lay on the window like butter.

Lucidos, what a beautiful fabric thank you, I've been looking online for UK stockists (I'm in Scotland). Would you also drape the linen around either of the side windows (each side of the large gable) or would you just put blinds on these? Would you stick to a natural colour for the blinds - hessian?

My plan for the room is very neutral at the moment: dark walnut flooring, rose white walls, oak roof beams and a neutral suite & matching stripy love seats (swatch pic attached). I'm thinking Plum would be a nice colour to add - plum cushions, ottoman and very light plum for the linen drapes - not sure if this will look ok.

Thank you

I would put them left and right of each set of rectangular windows, the door and any smaller windows in the room.

For a set up such as you have I would use a shade color close to the wall color then use a mid neutral color on the drapes, not the dark color. These drapes almost feel as they are floating and your window makes a huge statement in the room, you are right wanting to soften it. You want to minimize that statement to let the view do the talking not create another focal point that a dark color would establish.

Plum would be great integrated in the room against all those neutrals. Also some metals with a dull/aged patina.

What ever you do....do not do shtters...the view is too beautiful...this is going to take a good designer to do this treatment and it will cost to get the job done perfectly... We can do this for you as this one of our specialties. Also, we can have our workroom make the window treatments for you...so if you are interested call us.