We parked our car in an underground garage last summer when we spent 5 days in Paris. There are lots of garages with P signs leading the way. If you already know which hotel you'll be staying in, ask them for the nearest one. We parked below the Pantheon, which is not far from Notre Dame, and that particular garage is perhaps the biggest in that area.
We ended up paying a little over 20 eur per 24h period, which wasn't too bad, since it was easy and completely carefree.