Hi there and welcome to the forums,
From your description and the photo you have posted, your budgie doesn't look well at all. Usually when budgies show these symptoms they are already very sick and in need of emergency professional medical attention.
The best thing to do in this case is to book an emergency appointment with an avian vet specialist.
If your budgie hasn't been feeling well for a good while, I doubt there has been any recent mating attempts.
Is she currently able to feed herself? If not, you can keep her with her mate, but be aware that he will continue to be more exposed to whatever ailment your female budgie has.
It would be better to move her to a small hospital/travel cage and keep her warm by covering the cage on 3 sides.
If you have millet spray, you can soak it in electrolyte solution and offer it to her in hopes of giving her a little boost.
You can also offer her some egg food.
I truly hope you will be able to have her seen by an avian vet as soon as possible.