Upvote:4
It seems a no-brainer that if the visa says it does not allow you to travel to other Schengen countries, and supposing your nationality does not allow free entry for tourism purposes on Italy, that you have got to obtain a separate Italian tourist visa.
Your best bet is to visit the Italian embassy. However, to be on the safe side, first double-check with French authorities whether your current visa does allow you to re-entry in France.