Cut a length of timber the width of the window frame (or slightly wider if necessary), run a router around the ends and top to make it look pretty, then sit it on top of the window frame and mount it to the studs. That'll give you a nice solid point to attach the curtains to.

Edit: Going the whole hog with this idea and extending a box out from this mount to make a pelmet for the curtains is also an option, and one that will reduce energy loss too if you make it suitably resistant to air flow.

How wide is the window? How solid is the window frame?

It may depend on the type of curtain as well, eg curtain rod with light material vs hand drawn with 50kg velvet curtains

If it's not too wide, and the frame is solid, could you use bracket(s) that attach/extend from the blind brackets on the window frame? I've done some pretty wild stuff with angle brackets and various flat plates. Or I guess the young'uns would 3D print something...

What kind of blinds setup do you have? I can’t visualise it.

I have curtain hooks screwed into the outer front of a wooden frame and a bracket securing the blinds inside the frame.

There are two holes for screws that secure the blinds, and if the holes of both line up it might be possible to put them though a curtain hook bracket then through the holes for the blinds, holding them both on together by the same screw. (Obviously you’d want everything to be light. And not sure if it would hold well.)

However I have no idea of relative sizes or how it would actually align.

Plus if your setup is different or you get adjustable hooks where the lower part of the bracket obstructs the gap or the screw doesn’t pass through, I have to think of something else.

I thought this up after trying to find something similar to a double curtain rod hook but with blinds brackets, a combination of the two, however it seems what I was picturing might not exist.