Paris in the 19th century was as infamous for its pungent odor as it was for revolutionary riots. The streets were full of rubbish and horse dung, and anyone who was caught short in the open simply relieved themselves of where they stood.
To remedy this, the city's prefect Rambuteau ordered the construction of public urinals – phallic-looking structures with inbuilt plumbing that allow Paris' male population to urinate with relative dignity.
A simple cylindrical shape, made of masonry, open to the side of the road, and with an elaborately decorated cap on the other side, they were popularly known as 'colones rambuteau' ('Rambuteau column').
To protect his name from being associated with urinals, Rambuteau suggested the name 'Vespasianus', a reference to the first-century Roman emperor Titus Flavius Vespasianus, who taxed urine collected from public toilets for use in tanning. It is the term by which street urinals were known in the French-speaking world, not 'pisoire', a French-sounding term used in other countries.
As you can see from some of the photos, this solution didn't provide an enormous amount of privacy, but since the male's torso area was covered, it protected other Parisians from accidentally seeing someone's private parts. Plus, once the urine started to hold it helped clear the streets of dirt caused by stale urine.