How can I incorporate Python scripts into my website? Do I need a framework?
I completly agree with you about Django, but I think you can give a chance to Flask, it is really light and I can be used for many porpouses. Anyway if you want to call a python scripts you need a way to call it. I think you need a "listener" for the script for example a service or a web service (for this reason I think Flask can be an really easy solution).
Be careful about calling the script, a web service can be reachable from the frontend but this can not be done from a "standard" script.
My suggestion is take a look at Flask is more light that you think.
I'm wondering if there's a good way for me to incorporate Python scripts into my current website. 
I have a personal website & my own server that I have been working with for a while. So far it's just been html / css / javascript. I have made a Python script in the past that uses another website's API to retrieve something that I would like to display on my website. I've only used Python from the terminal to take input and spit out results. Is there a way for me to run a Python script from javascript through Ajax to get some content back? 
I don't really want to use a framework like Django or Flask because I feel as though those are mostly for entire projects. I only want to use one Python script on one page for my website. Is this even something I should do? Any advice would be great.