Is there a way to restore the cycles render settings to default?

If I understand your question, I don't think there is.

You can load a .blend file without the saved UI, but this doesn't include settings in the render property panel (which is what I think you are getting at). These cannot (as far as I know) be divorced from the other data in the file.

You would probably need to create a new empty file (which should load default settings for everything), and then use File->Append to import the objects from your other .blend file into that new file.