Baggage Check at Notre Dame

There are left luggage counters/lockers at major train stations. If you are arriving at CDG and taking the RER to Gare du Nord, you could check your bag at the left luggage in Gare du Nord.

When you say "carry-on sized back-packs," I'm assuming this is your luggage for the trip. That being said..... I don't think you'll have any problem with Notre Dame. Unfortunately, I don't recall any place to check them there. Other than the inconvenience, I think you'll be fine but you probably won't be climbing the tower. Ste Chapelle is a totally different story. It's in the same complex as the French version of the US Supreme Court. There is a very thorough security check there. I don't know if you can even go through with what would look like luggage. Even if you could, it would be a pain dragging them up to the top floor in Ste Chapelle. Perhaps you should go there another day. The Historic Paris Walk is about 3 hours tops plus any time you want to spend eating lunch. You'll probably still have a few hours to kill waiting for the appointment at the apartment.

Hannah, I'd suggest contacting the people with the apartment, as they may be willing to store your luggage for a few hours, which would save you the cost of a Locker (however it's important to ensure that they have a "secure" location for storage). Most places are willing to do that, and they may even put the bags in your room when it's ready. At least with Hotels and Hostels, I've found that rooms are often cleaned and available earlier than the time they state. Happy travels!

Just a little tip-I found Notre Dame a nice place to sit for a while. You might even be able to get a little nap.

There's no bag check or storage at Notre Dame Cathedral. Sharp or pointed metal objects (knives, scissors, etc) aren't allowed into Sainte-Chapelle. If I were you I'd do what Canada Ken suggested.