A plaque on the front of the building shows that it was run by an organisation called the Societé Philanthropique (who still manage the building today), and the city of Paris have helpfully put a sign in the street outside giving an outline of the story, but what is most striking about the structure is the rough brickwork of the facade. This is social housing at its most basic, clean and functional accommodation, but devoid of any decorative features that may have encouraged the poor to stay a little too long.
It was a rich banker named Michel Heine who paid for this construction through his Fondation Heine charity. He donated 600,000 Francs to the Societé Philanthropique and asked them to build a home for the 'deserving poor'. This was very much the philosophy of the Societé Philanthropique who believed (and apparently still believe) in helping the poor to help themselves, funding projects that help people get through difficult moments, to rebuild lives, or simply where the old could see out the rest of their days in dignity.
Michel Heine was an interesting man, somebody who spent many years in the USA and married into the Richelieu dynasty (he was eventually buried in the family tomb). He knew and gave financial support to Sarah Bernhardt, calling her his 'cochon doré' (golden pig!). Heine's reaction to the building he financed is not documented, but it is possible that it was severe enough to ensure that no such buildings were put up again. Later constructions managed by the Societé Philanthropique all contained decorative elements, and it is suspected that the rich benefactors who paid for them did not want to be associated with such basic, functional structures. After all, it was their names which were often featured at the entrance.
For more details on this building, see my post on Bricks in Paris.