Just returned from 2 weeks based in Paris and report as follows:
"Found Ring Scam" - occurred twice a week apart, both times on the footbridge over the Seine by the Orsay. Harmless and easily deflected.
"Friendship Bracelet Scam" - narrowly avoided on the steps below Sacre Couer. Two very aggressive men would approach and try to get the bracelet on your wrist before you could react and pull your arm back. They were very pushy and intimidating, grabbing people by the shoulder as they walked past trying to avoid them. This is the only time I felt physically at risk during my stay.
Metro - no problems, but vigilant and on guard and never carrying anything more than a day pack.
Major site security - many sites (Notre Dame, Orsay, Montparnass train station, etc.). Besides police, each site had three soldiers in fatigues carrying assault rifles, slowly and seriously patrolling in a triangle formation. Both disconcerting and reassuring, given current events.
Ed in Seattle, WA