Your bags will be checked through. BUT, you will clear immigration in CDG not in FCO. Italy and France are part of "Shengen" Europe, so there is no doubt about that. All FCO flights arrive at CDG in the Shengen area.
That being said, France has periodically installed some immigration controls on fights arriving from some Shengen countries. I do not know where it currently stands. But you will have to clear immigration to exit Europe at CDG before departing to the US. It is usually fast going out.