Im currently evaluating Drupal to see if we can use it to replace our framework. My problem is I have this legacy tables which I would want to try to reflect in Drupal. It involves a join table. There’s quite a lot of this kind of relationship in our existing web app so I am looking for possible ways to solve it.

Thank you for your insight!
There are several ways to do this, and it’s hard to know which is best with no context about what you’re actually doing with the data, but here are some options:
One way to do this is to make a content type representing each table (using CCK) with the foreign keys represented by type-specific node reference fields. Doing everything as nodes gives you a bunch of prebuilt functionality around nodes, but has a bit of overhead you may want to avoid.
Another option is to leave your database just like it is now. Drupal can do direct database queries, or you can use Data to expose your tables to Views.
Another option, if those referenced tables really only have 1 non-ID field, is to do the project_companies_assignments as nodes and do the other 3 as taxonomies. But this won’t work if those are really more complex entities, and wouldn’t be very flexible if they might become more complex.