What happened after the ban?
Most of the great absinthe-producing firms went bankrupt, or amalgamated, or switched to producing pastis. Some firms transferred their production to Spain, where absinthe was never banned, and where it continued to be made on a small scale for the next century. A remnant of the Pernod company made absinthe in Tarragona from 1918 until the mid '60's, although by 1950 the product had already deviated quite considerably from the pre-ban French original.
In the Val de Travers region of Switzerland, production of the local uncoloured "Le Bleue" went underground, and fairly large scale bootlegging operations continued up to 2005, when absinthe was once again made legal. In many countries though absinthe was never formally prohibited – it just faded from sight.
Absinthe has never been banned in the UK, nor in much of Southern and Eastern Europe.