The technical name of the wormwood plant is Artemisia absinthium.  Is there thus a connection between wormwood and the popular French drink absinthe?
The ever helpful “The Wormwood Society—America’s Premier Absinthe Association and Information Network” explains on its FAQ page: Absinthe is an anise and wormwood flavored distilled spirit, made from aniseed, fennel and wormwood.  
Traditionally, absinthe in France has been a working class drink, especially popular in the South, and associated with melancholy rather than exuberance. Edgar Degas said it best: