Peugeot 307 indicator.

Probably a faulty BSI,
Or body systems interface,
Controls all the electrics.
Only way to be sure is a Global Test with Peugeot's own diagnostics Peugeot Planet.
Or remove the BSI and send it of for testing.
Oh and they're vehicle coded so used parts wont work.

have you checked the connectors to front and rear indicators for damp and corrosion on connectors also any earth connections to lights do the hazard lights work and also would advise checking flasher unit I would first unplug hazard light switch see if light goes out second check flasher unit by disconnecting