The integration of phpBB and Joomla 1.0.x is possible, although it rarely works properly.
This is why the best solution for Joomla 1.0.x is to use a stand-alone forum component. The most popular forum component for Joomla 1.0.x is FireBoard. It is installed as any other Joomla component and it offers all features that you would expect from a forum application.