Paris is generally safe EXCEPT for pickpockets who are EVERYWHERE. You'll spot them not just in subways but also a particular favorite haunt of these parasites: escalators and stairs. They're skillful and also brazen. Do not put anything in your bag, purse, backpack and/or pocket that you're not OK to lose.
So enjoy Paris as it is certainly one of the most beautiul cities in the world, but beware! beware!