Ashley

Nah charcoal doesn't fix by itself. You can get fixative sprays in art shops (specifically meant for charcoal on paper), or you can try using hairspray (might end up a bit sticky maybe, depending on the hairspray, but it should be fine). Just make sure you spray it from a decent distance, otherwise you'll get spots/blotches. And do it in a nicely ventilated room, cause it smells. =P

Also, it's likely one layer won't be enough. So spray on one layer now, then wait until it's dry and spray on another layer. That way you can be sure it won't smudge anymore. =)