I am planning on applying a tint film to reduce the heat entering the house in summer as well as reduce damage to the floor and furniture, but the Australian sun is so harsh it requires a lot more to block it out :(

Absolutely you can mix traditional windows with contemporary window treatments, although I don't think plantations are considered contemporary by any means. Ordinarily sash windows can have shutters installed over them, however I can see your sill is very narrow given your bottom pane sits forward of the frame. I can see privacy is no issue, in fact you have a great view and half height windows allow light in and keep peepers out, so I suggest plantation shutters fitted to your French doors, to allow tilt and directional light and a roman blind as the folds of fabric mimic the frames themselves to your corner arrangement. If they are too fussy for you a standard holland blind, however be creative, you can have a bonded holland which allows for a fabric front bonded to a block out backing, you can ask for a roman fold on the bottom making them look like a roman when rolled almost all up, and dress the window a little better, but Hollands can roll up into the frame and allow for maximum window when wanted.

No be fine :)

I had similar dilemna and painted all woodwork including doors etc white, which I am happy with, it all ties together well.