As you can see in this image, the outlines are slighty darker than the material they surround. How can I do something like that in Blender (Render mode)?
With the Freestyle rendering option enabled, you will find the Freestyle Line panel showing up in the Material properties window. The color selector in this panel allows you to choose a line color associated to the material. The line color can then be referenced using the Material color modifier in the Freestyle Line Style panel in the Render Layers properties window.
At material boundaries, you might want to use the Priority parameter in the Freestyle Line panel to give a precedence to one of two competing line colors at material boundaries. A post in the Freestyle development blog details this feature if you're interested.
Here is a pretty easy setup to play with.
Change your material to have a custom color on the edge of the fresnel fall-off. I did this with two diffuse nodes, one grey for the main portion of my objects, and one a green color, and then used a mix node with the factor being my fresnel output.
Play with the Fresnel value to your liking.
"Green-Screen" out your green in the compositor with chroma key.
"Alpha Over" this chroma keyed image under a multi colored image (could also be an image strip for some pretty cool effects), by a factor being driven by the Matte output of the Chroma Key.
If you want to fine tune this, then start playing with the Cutoff value in the Chroma Key Node.
Using the freestyle lines in a color that will change according to what is underneath when using 'Multiply' as a color mix mode in the compositor is a possibility. You could use a gray value that will be a darker value of each color, though you won't arrive at a black outline this way in your final composite. and the file