Apart from taking the usual care is it in general safe to be around after dark? I want to shoot but not get shot or mugged!
I don't remember feeling unsafe anywhere, though I wouldn't want to be around Les Halles late at night. Then again, that's just my gut feeling from two short holiday visits, so people with more experience of Paris may tell you otherwise.
The area around Notre Dame was pretty lively even at midnight (might have been a weekend night, I don't quite remember), as was the area around the Eiffel Tower a bit earlier. The Louvre is open until 10 p.m. twice a week, so for better or for worse there will be folk milling around there for a while after. Along the river was fine too. The area around the Grand Palais (a building I'm oddly fascinated with) was fairly deserted at night, but I didn't feel unsafe there either.
So basically, from my experience, I'd say it's pretty safe, at least in the centre/touristy areas I visited. If anything, I'd worry more about pickpockets around railway stations or other crowded areas (not that I encountered any myself).