This particular fat-face might not be digitized.
So far, I have not found many with Didot serifs at and only at the locations in your image.
For example Standard Poster by ParaType
http://www.myfonts.com/fonts/paratype/standard-poster/
Normande BQ
http://www.myfonts.com/fonts/berthold/normande-bq/
Don

...it's also close to Bodoni D Black by URW++

Hi Fivos, yes the Bodoni D Black by URW++ seems the closest so far.
Don

Thank you all for your much appreciated help!