How long are you going to be staying / needing a locker?
I haven't stayed there but several people recommend the BVJ Louvre. I don't know if it has private lockers though, sorry.
Most hostels have a locked luggage storage room. Just make sure that you have a decent lock on your bags and they should be fine in there.
Try calling around to the places you're interested in and ask someone about it, that may be the best way to find out for sure (unless someone replies here with a recommendation, that is).