Fourvière hill is where the Romans set up Lugnudum (their name for Lyon) and contains the treasures of Cathédrale St Jean, Basillique Notre Dame de Fourvière, Place St Jean, Rue St Jean and a Roman amphitheatre.
Just take the funicular from the bottom of Fourvière hill up to Basillique Notre or walk up from Cathédrale St Jean and lose yourself in the alleyways and squares of old Lyon.
Fourvière hill lies on the left bank of the Saone river opposite Presqu'ile. From Place Bellecour just follow the signs for Fourvière.
Updates
Is this your business?
Fourvière = the area on top of the hill, including the Basilique Notre-Dame de Fourvière and the Roman theatres.
Vieux Lyon (incorporating the three districts of St Paul to the north, St Jean in the centre and St Georges to the south) = the area at the foot of the hill next to the River Saône, and including the Cathédrale St Jean and the old streets, renaissance architecture and traboules.