I've had this problem before. The trouble is that whatever you use to remove the gold paint is likely
to remove the original gilding. White spirit might shift some of it, but it would be a extremely tedious
job given the ornate bits. Acetone would be quicker but it would strip the frame down to the gesso.
Try white spirit on a soft rag and rub gently to see if the paint comes of without effecting the gilding
beneath. It's worth a try. If that doesn't work I fear you are stuffed.
Essentially, whoever thought it was a good idea to slap on a coat of paint ruined the frame.