Have you got this?
From the Paris Archives.
(On MyHeritage)
My French is not good enough to translate some bits of it - you could post it on the Europe board here on Rootschat where no doubt somebody will be able to.
There seems to be a Marie Clementine Augustine Couppey as the mother of Augustine Victorine, and a Clementine Couppey - are they the same person?
As I say, my French is not good enough to make out some of it.
I suspect all the people named near the end are witnesses to this document.
From this and all the familytrees on familysearch and MyHeritage, it does look as though she was an illegitimate daughter of Clementine, so there may not be any records with his name on.
Unless there was some system in France at that time for 'child support'.
Added:
I see you managed to find the original Neale while I was finding this.
Worth having both documents though - you never know what clues might be there.