Start with a regular old part down the middle, putting one side in a temporary pigtail.
Coming off of the center part a little ways back, part out a rectangular section of hair. Take the top inch or two of that section and clip it or flip it over to the other side to keep it out of the way for now.Take the hair you have left, brush it up towards the top of her head and braid it. (This may seem a little awkward since normally you would be braiding downwards.) It needs to go upwards to lay flat against her head though.
Repeat these steps on the other side of her head. You should now have 2 braids, one on each side. Split the 2 sections you left out earlier in half and lay the braids through the sections, over the top of her head.
Comb everything smooth and spray with a little water. To start the french braids: Make your first 3 sections by grabbing the hair on either side of the braids, then split each side in 2 (4 sections) now combine the middle pieces to make 3 pieces. It will lay much smoother if you start it this way.
French braid like you normally would. The braid hanging down on each side will just become part of the french braid. You won't even notice it. Just make sure to take the elastic on the end of the braid out if you don't want it poking through. The french braid will hold the braid in place and keep it from unraveling, so you don't need the elastic.
Normally I make the headband up closer to the front of her head. It's more noticeable that way.
Btw, if you don't know how to french braid, you could use this same concept with regular pigtail braids ("indian braids.") The hair you're working with would need to be fairly long to go all the way over the top and down the sides of her head though.
And, since many of you have requested a video tutorial for this style... here you are, enjoy!