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Without knowing exactly how your application is set up, I can’t really say exactly how to solve this problem.
I can tell you that it’s quite common to use two web servers with Django – one handles the static content, and reverse proxies everything else to a different port where the Django app is listening. Restarting the normal HTTP daemon therefore wouldn’t affect the Django app, so you need to restart the one handling the Django app. Until you restart it, the prior version of the code will be running.
I generally use Nginx as my static server and Gunicorn with the Django app, with Supervisor used to run Gunicorn, and this is a common setup. I recommend you take a look at the config for the main web server to see if it forwards anything to another port. If so, you need to see what server is running on that port and restart it.
Also, is there a Fabric configuration (fabfile.py)? A lot of people use Fabric to automate Django deployments, and if there is one then there may be a command already defined for deploying.