One thing I know about spending time in Paris is that the metro system constantly reminds you to keep your belongings close and watch out for pickpocketers.
Even after doing this, I still left the metro missing a gift bag with a necklace I bought from the Louvre Museum. I had two friends with me standing alongside me while holding the railing in the metro. I sat next to an older French woman as I was talking to my friends from beside her. I was holding my gift bag and she offered to switch seats with me so that I could be closer to my friends. I said sure without thinking anything of it, although something in my mind told me not to do it. Follow your gut folks! I did not even realize that I was no longer holding my gift bag and when I got up from the seat to leave there was nothing left in my seat. The woman was gone, and it took me seconds before I realized that I did not have my belongings anymore. I was devastated and felt like an absolute fool. My advice to anyone who decides to take the metro is to make sure that their belongings stay in front of them, whether it be a purse or bag. I would say keep that purse in the front, not on the side of you, and anything you can put on your body. For example, I should have put the necklace on instead of holding it in the gift bag. Finally, I advise that you do not put important items in open pockets unless they are inside pockets.
With all of that being said, watch out for pickpocketers and enjoy the metro!