(Multi-part post):
I've been to Paris loads of time, usually on day trips (with Eurostar) and usually arriving and departing at around the same times as you will be. So here are a few suggestions for you:
I'm guessing that you'll be arriving on Eurostar. If so, take the RER Line B, southbound (i.e. towards Robinson and Saint-R�my-l�s-Chevreuse) from Gare du Nord, to St-Michel-Notre-Dame. If you want to view Notre Dame Cathedral, just follow the signs from the station.
Alternatively (or afterwards) walk into the Latin Quarter, which commences immediately south of the station. If you walk along the Boulevard Saint Michel, and explore the side streets which run off it, you'll find an eclectic assortment of shops. If the weather's fine, you might want to wander into the attractive Parc du Luxembourg, which you'll find on the right hand side of the Boulevard Saint Michel. The French Senate building, the Palais du Luxembourg, is in the park and is well worth a photograph or two. Alternatively, taking the side streets off of the Boulevard Saint Michel, opposite the Parc du Luxembourg, will take you to the Pantheon.