The Glomar Explorer supposedly raised a Soviet Sub back in the 1960's or earlier.
We do have UUV's, MUV's and other things that can go that deep.
But they need to assemble this ASAP or borrow it ASAP (if the US Navy is not going to do it).
I am not sure what resources France has in this regards, but if the US Navy chose to make this an important training exercise, it could be found before the 30 days -- at least my belief...
I believe the French were bringing in mini-subs that could go down far enough to retrieve the black box. I also thought I read that the U.S. had been asked for help. I don’t know what King Zero’s response was, though.
Going back to Cousteau, the French have all been pretty cutting edge with the dive stuff. They're really into deep sea for some Frenchie reason. They'll have very good submersibles available.