As is often the case in such examples, the origin of this property seems to have been a dispute. Originally the gap between the two buildings (situated opposite the town hall of the 10th arrondissment and alongside the Marché Saint Martin) was a narrow passageway, but following a disagreement about ownership and access, one of the parties decided to end the argument by filling the space with a new property.
The property was officially recognised with its own number in the street, but was never really more than a tiny shop unit at ground level (originally a shoemaker) with a room above, which actually connects to the first-floor property at number 41.
A newspaper article at the end of the 19th century describes the property, pointing out that the room was home to a baby, the cot apparently taking up the entire space. Peeking up into the open window on the day I passed recently, it seems that it has more recently been converted into a kitchen.
More mysterious is the wall above the property and its strange wooden shutter. No mention is made of an additional floor to the property anywhere, so it must belong to another building behind. Exactly what form that building takes or what its purpose is though is not clear, and Google Maps is of little help.
With two rather smart properties on either side, which presumably have rear windows too, it would be difficult to imagine a building any larger than the one that is visible. Is there then a second tiny property above or behind the city's smallest house?