How do I find somebody to stay in my apartment in Paris during August?

You can post it to local school forums and intern sites. Your best bet may be to try airbnb.com though. They let you list the dates that your apartment will be available and then people can book it kind of like a hotel, you set the price per night so you could maybe even end up making more then your rent costs. Especially in such a tourist spot like Paris. Might be worth a shot.