Originally the catacombs were stone quarries, which produced much of the stone that helped build the city.

In the 18th century had a huge problem with cemeteries, both the traditional kind and the open pits for the commoners (this is beautifully described in Patrick Suskind's novel Perfume). The problems linked to the stench and sanitary risks were confirmed by the Royal Academy of Sciences in 1737 (after close to 200 years of reports from the medical community).

In 1780, the weight of the decomposed bodies of one of the open common graves broke down the wall of a neighboring building's cellar. This added to the cost of maintaining the pits made closing these cemeteries necessary.

From 1785 up until 1814 many parisian cemeteries are emptied and the bodies transferred to the quarries. This process was of course under the supervision of the Church and the Ministry of Religion.

The inscriptions you refer to are usually found in the ossuary. The most famous one marks its entrance with "Arrête C'est ici l'empire de la mort" ("Stop, here is the empire of death") writtent by Jacques Delille. The reason for the spectacular display is generally said to be to force respect and generate some level of fear of God in visitors (quite typical in the romantico-macabre style - similar to what can be found in the Sedlec Ossuary in the Czech Republic).

Source : Patrick Saletta "a la découverte des souterrains de paris" and the "Atlas du Paris Souterrain" (as well as documentation from the city of Paris but that's not really a source is it?)