To some extent, they would be justified in believing that. The US has a homicide rate more than three times as high as France, and France actually has a fairly high rate of violent crime compared to most of Europe. There are only a small number of localities in the US that would qualify as safe by European standards.

Not for the whole country. Most of europeans never heard of "gated communities". However they may get from the news (from the google bus and stars/hollywood stories for example) that the inequality gap between rich and poor is quickly widening in some regions of California. Hence those who heard of gated communities may believe they are frequent in this particular state at least.