I'd probably put the door flush with the front of that opening (side toward us in the pix). Then you have about 8 more inches you could turn into a book case, or a concealed storage area for guns or other valuables. Or a narrow bookcase might fit there. I am fond of French doors. Not sure of the wide opening size, but we have a 60 inch wide set of double french doors that really look great. Then you could put another French door or a conventional door in the other entrance. Install some sort of curtain behind the glass so you have a little bit of privacy, or in case you have trouble keeping things tidy.
You have to be very careful aligning the doors on a double door set. The installer we had couldn't get it aligned correctly and kept installing screws through the same opening, which was what was pulling it out of alignment. Getting the frame plumb is critical. If I were installing double doors, I'd set them back further into the opening, That recess will really set the room apart and be very inviting.The other side of the opening should be flush with the outside wall and gives you space for a built-in book case. Nice to have an office.
The more I do, the less I accomplish.