Double check your bluetooth settings. I can select bluetooth for calls and also media.
Set your phone up playing a track over its speaker. Then turn on your ignition. On my car (fiat) it takes about 30 seconds for the phone audio to connect and I get a visual indication on the cars display when the connection is made and the sound then outputs over the car speakers.
Early Peugeot Bluetooth modules from about 2006 to 2010 only support Hands Free and have no support for Bluetooth Music Streaming. Cars post 2010 had a later Bluetooth module that does support Bluetooth Music Streaming. This module cannot be fitted to earlier cars as Peugeot updated the CAN bus to CAN+ bus in about 2010 and the two system are not compatible so modules cannot be supported on both systems.