What drove the Puy de Dôme volcano?
According the an Oregon State website, 


  Volcanism far from the edges of tectonic plates, such as Chaine des
  Puys, is rare. Changes in the mantle may have led to volcanism at
  Chaine des Puys. Several lines of evidence indicate thinning of the
  crust and upwelling of the asthenosphere. The rising mantle "diapir"
  was probably a total of 30-60 miles (50-100 km) in diameter.


Chain des Puys is the 40km long chain of volcanic features to which Puy de Dome belongs. It sounds like the causes are not completely understood. Unfortunately, all the papers I could find on the topic are in French (understandably), so if you can read French you can try Google Scholar to see if there is more info there.