We lived in downtown Paris for many years.
We were there during the 2005 riots and were confused when friends from the US asked if we were coming home; there was nothing going on downtown where we lived. The "Paris riots" were actually 15 miles away so while there were riots going on, we were sipping coffee on a sidewalk.
Strikes, 'riots', car burning and rock throwing is a fairly commonplace thing there but it is generally localized and not usually in the tourist areas like this is. Almost every weekend downtown there is some road closure due to a demonstration against something; 500 people walking around with bullhorns and flags.
I called some friends today. They're pretty sanguine about it (typical French!) but didn't really comment on the validity of the issue.
Our personal experience:
Back in 2005 CNN kept repeating a montage of burning cars, rock throwers and Champs Elysee being barricaded with crowd control fences; implication being that the barricades were for the riots on the Champs. The only problem is that the barricades on the Champs was for a Veterans Day parade and had nothing to do with the riots.
So...we tend to take these things with a grain of salt. Not to say that it isn't serious...but it may be a bit overblown by the media.
The closing of the Eiffel tower is a regular occurrence as are cops carrying machine guns.
We do feel bad for tourists on their 'once in a lifetime' visit; sad.