I have traveled to Paris on several occassions and have never had a problem. Despite the general perception that the French people are rude I have found them to be very nice and helpful on many occassions both in and outside of Paris. I actually feel safer walking around Paris at night than I do walking around most cities in the US. I have frequently walked around Paris alone at 2AM with little apprehension compared to doing the same in LA, NYC, San Fran, Miami, etc. The police in Paris have always been very friendly towards me, actually more so after they knew I was an American. However, I still would not advertise that you are American.

I don't know if you have ever been to Paris before but if not the Metro system (subway) is very good in terms of alternate routes. You can literally get anywhere in the city via several different routes using the Metro so you can use it to avoid areas where there may be problems.

Likewise I would get a good street map of Paris and orient yourself with the monuments and the river. Between the monuments and the river it is very easy to stay oriented when walking the streets and navigate the city even in areas you may not be familiar with.

IMO The central city itself is actually much safer than the outskirts where the muslim housing projects are so if you have to travel outside of the city be extremely careful. The riots a few years ago when they were burning the busses and cars were mainly in the outskirts of Paris.

As I recall the last time I looked up the statutes, carrying just about any type of weapon (including knives) in Paris is a big no-no however you may want to consider improvised weapons such as a nicely sharpened pencil for a stabbing weapon or a good strong flashlight for an impact weapon both would seem to be easily explainable to the local police if need be.