I would go with none. Or something very, very minimal.

I have French doors in my bedroom, and I need window coverings for privacy and light control. Also, the view just outside the doors is not all that great. I use a double rod with a layer of sheers and a layer of heavier, more opaque curtains. They suit my purposes well enough. Both the sheers and the curtains hang from rings, and I left enough space between the end of the rods and the hinges of the doors that I can draw the coverings well to the sides if I want to keep my doors open. By the way, I like your curtain panels with the trellis pattern much better than the solid ones on the right. Good luck!

Thanks! Although not showing in my pics, we do have a beautiful wooded view outside our doors. I like the open look and so does my husband, except when it gets dark early in winter, then he likes to draw curtains or blinds closed.
Glad you liked the trellis pattern panel. I wasn't sure about mixing that pattern with the rug.

https://www.overstock.com/Home-Garden/Blinds-Shades/6423/subcat.html?featuredproduct=11749994&featuredoption=18304830&cid=202290&kid=9553000357392&track=pspla&ci_src=17588969&ci_sku=18666045-000-00192700020716580115&gclid=CjwKEAjw-LLKBRCdhqmwtYmX93kSJAAORDM6PViYILLZTCcOclRKwB8AiBoKR7eVKTNBM8rg7tJABRoCiqrw_wcB&gclsrc=aw.ds&dclid=CNP0uYTh1dQCFVKfAQodI0oJRw

Not sure what your budget is, but there are new shutter sliders that could be really perfect for this application. They are "shutters" but in panels and they slide across the space beautifully. Personally, drapery at sliders are very difficult to keep looking right due to wind and soils blowing in from outside if you use the slider a lot. Even when hanging rod as Liz H mentioned above. Might want to check those out. I don't have a source right in front of me, but you can google "shutters on panels for slider doors" and some will come up.

Thanks for the link and new option to consider.

LOVE the sliding shutters Flo Mangan, but not in the budget at this time.

Sure, they are pricey. Perhaps the sliding panels are an option.