Both are currently open with no doors.

Your home appears to have traditional, formal, room arrangement. Don't muck about with anything modern. Reduce size of both openings equally. (Reserve casement trim as you may not be able to match) add french doors with divided panes. Doors on one room is fine (reminiscent of the old-style parlor), or do both.

What is the height of the doors further down the hallway let's say for a closet? You should be consistent on door heights, but I see no reason to have to place doors on either side to match. That said, I would purchase French doors with matching transom and sidelights to meet your size.

Here are three options for French doors, transoms and sidelights. You order the complete unit and the carpenter installs it.

The other doors on that level are 80". I also thought about the transom and sidelights, but had trouble finding sets in my search like you provided.

Take the picture to Lowes, HD or a lumberyard and ask them to quote you a price. But if you're having a carpenter do the install have him decide on the right size to order.

I like the first option BeverlyFLADeziner suggested.