Thank you very much. I should have explained better. It's not a full wall, it is 31" deep from the rear wall that runs behind the fridge to the doorway to the dining room. Here is a photo of my current fridge and that (partial) wall:

Current fridge is 29" deep including the door, 31" wide and there are a few inches on either side for stashing the broom and perpetually losing things that fall from the counter ;-)

The counter-depth fridge in question is 36" wide, the body without doors is 23.8 " and the total depth of the fridge with doors closed is 28.5. The total width of the space is 38.5 inches.

I suggest a 6" or 9" pullout. 6" is probably fine, but 9" would be "safer" and give you better storage options. As an example, you could have a utility pullout for a broom, dustpan, etc.

The manufacturer specs should specify the distance required.

numbersjunkie, thank you. I could not find the info in the specs listed on the Home Depot page, but I found this posted by Frigidaire support in the Q and A about having the fridge near a wall:

Unit model FGHC2331PF requires a specification of 45" of depth to be able to open the door at 90° angle.

Unfortunately, I don't understand what this means. It doesn't make sense that the fridge would need a space 45" deep from back to front. Do they mean the fridge needs nothing poking out further than the counters for 45" total from left to right?

I don't know if this helps. Our french door counter-depth....the walls on either side of the fridge (one is a drywall 4.5" thick and the other is a cabinet side of about 1/2" thick) are the depth of the fridge without the doors. Both doors will not open 180 degrees, but about 150 degrees. The space between the fridge and walls is about 1/4" or less.

Thanks. I think I will have to go look at the fridge to see how far the doors have to open in order to get drawers out, and judge from that. With our current fridge, we cannot remove the drawer nearest the door hinge without opening the door past 45 degrees, but it doesn't have to be fully open, either.

I went and looked at the fridge today. I don't think it will work for our space. The crisper drawers cannot come out with the door open as far as we'd be able to open it here. I don't have to have a new fridge, so I'm not going to worry about it now and hopefully will find a smaller one when the day comes. Thank you all for your suggestions!