I have uploaded my products to the Facebook catalogue manager, all good there.
I am running some ads promoting products.
Once the user clicks through to the product, they get the option to "check out on website" at which point they are redirected to my site.
My question is, is there any way that I can change the settings so that they can check out on Facebook?
Short answer, depends on where you're based.
The checkout on Facebook (or Instagram) feature is only available for businesses with US bank accounts at the moment, and is expected to roll-out for the rest of the world soon(?). If it is available to you, then you can set it up through your Commerce Manager section on your Facebook account's Business Manager, by following the setup process.