Could be completely wrong.
But - my photos of Frenchmans from the Irenabyss track back at the saddle indicate some remote possibilities - but the problem is your background.
Your photo picks up not only the "hole" but a chasm beyond with another wall at the back.
So I would like to suggest this ringed location from a zoom photo at Barron Pass.

- Face of the Frenchman from Barron Pass - with ring around the possible site of the hole
It is actually a bit below a spot where we left the main track near the top to get a better view over Barron Pass and Lake Tahune at the same time.
I think the peninsula to its right is your background wall. [I think people might base jump from that to land over Lake Tahune.]
If so - we did not see it, but might have if we had looked more closely into the chasm. It would not be far from the main track at all.
If that is the spot - then this photo would have been taken from above it.

- Above chasm looking back to Tahune over the gendarm