I have built an application in python that is hosted on heroku which basically uses a script written in Python to store some results into a database (it runs as a scheduled task on daily basis). I would have done this with ruby/rails to avoid this confusion, but the application partner did not support Ruby.
I would like to know if it will be possible to build the front-end with Ruby on Rails and use the same database. 
My rails application will need to make use MVC and have its own tables on the database, but it will also use the database that python sends data to just to retrieve some data from there.
Can I create the Rails app and reference the details of the database that my python application uses?
How could I test this on my local machine?
What would be the best approach to this?
I don't see any problem in doing this, as far as rails manages the database structure and python script populates it with data.
My advice, but just to make it simpler, is to define the database schema through migrations in your rails app and build it like the python script doesn't exist.
Once you have completed it, simply start the python script so it can start populating the Database (could be necessary to rename some table in the python script, but no more than this).
If you want to test in your local machine you can one of this:

run the python script in your local machine
configure the database.ymlin your rails app to point to the remote DB (can be difficult if you don't have administration access to the host server, because of port farwarding etc)

The only thing you should keep in mind is about concurrent accesses.
Because you have 2 application that both read and write in your DB, would be better if the python script makes its job in a single and atomic transaction, to avoid your rails app finding the DB in an half-updated state.
You can see the database like a shared box, it doesn't matter how many applications use it.
Rails app to work with a remote heroku database