What you see on the photo is the tracks of a railway system constructed 1852 - 1897, running partly over and partly underground, who transported up to 39.000.000 passengers during the World Expo 1900. (petite ceinture = little belt)
Due to the Metro network becoming better and better, it lost its passengers over the years and was made redundant in 1934 and replaced by buses. Little parts of it were still active until 1985, other parts were used by other trains. Many people tried to save it, some organised special train rides to remember the old days, but it happens rarely nowadays.
Paris' public transport system (RATP) is since some years working on a tram system, that will now replace the buses that replaced this once highly frequented train line. Some then opted for a relaunch of the petite ceinture, but it never happened.
Some train stations have disappeared, others been transformed to stock places, police stations or even a concert hall (see Flèche d'Or). The underground areas are sometimes squatted.
It is funny to follow it's traces, to see how it pops out in Buttes Chaumont park or other places, here are some ENTRY SPOTS to the tracks. Be a group and be careful, good shoes and good torches are recommended. And bear in mind that you are actually doing something illegal !!!
An association who tries to save the petite ceinture.
More info and photos of some old train stations.
Flèche d'Or - a club housed in a former train station
Buttes-Chaumont Park