After you get the basic technique of a french braid, you can change the look in a lot of different ways. Here are a couple examples.
This is just simple french braids with a part in the middle, but see how it changes the look when you make the sections of "add in" hair narrow:
You could also make the sections very wide. That will make the braiding go quicker and give it more of a casual look, but I don't have a picture of that. Here is a single diagonal french braid:
The tail is over her shoulder in this picture, even though it looks like it is gone. If the hair is not too long, you can do a sort of loose french braid and tuck the end up inside. The underside of the braid makes a tunnel the tail can fit into, and it looks just like this above. Bobby pins might be needed to keep it from falling out. To form a diagonal going to the right, whenever you add hair from the right side, gather hair up to the edge of the braid, and do not collect hair underneath the braid. When collecting hair from the left, gather it all the way across the side and under the braid. You could also have your "subject" tilt her head to the side so you can just braid it as if it were straight. Here is a diagram of how the pieces were collected in this braid. Hope this helps.