Whoa, you want 36-foot wide fridge?!?
(I'm sorry, I just can't resist when I see someone write 36' instead of 36")

ANYWAY! I'm not sure if there is one. I think there used to be. You can still find some Marvel-branded ones out there.

The ones I've seen are just re-badged fridges by Amana, very similar to most KA, Maytag, etc, you'd see out there.
The Viking freestanding counter-depth is the same too.

Do you specifically want an AGA fridge because you have an AGA range and want to match them up?
Or have you found an AGA one and you're just checking if it's decent?

The software here forces feet (changes the inches sign to foot sign)...no one does this intentionally (though if I could get one and have a house big enough, I would LOVE IT ;-) ).

Liebher and AGA were the only "true" 24" deep fridges...I am not locked in. My LG is making noises and I am getting ready.

Sorry AGA does still have their 36" fridge:
http://www.aga-ranges.com/_store/Scripts/prodview.asp?idproduct=160

It's not a french door though. Bottom-mount freezer with a single left-hinge or right-hinge door above.

And there are others too.
There are multiple KitchenAid & Jenn-Air models that are freestanding and counter-depth.
Elecrolux Icon has a 24" deep SxS. With their nice french door model, the cabinet is counter-depth with the doors extending past by about 2". (But avoid the Elux models with in-door water dispenser.)

If your budget & cabinet layout allows, there are numerous built-in options.

Do you have a budget in mind?

Here is a link that might be useful: AGA 36