I am a professional tour director and my work takes me all over the world. I currently live in the United States but I would like to move to Italy. It will take some time for me to get an permanent visa but my work would probably ensure that I am not in Italy for more than 90 days in an 180 day period. It's a lot to juggle though and would mean turning down jobs in Italy so as not to go over my allotted time. Which would be a shame because I do speak Italian. However, I do have two passports. Would I be able to enter Italy on my US passport, hit the 90 day mark, head to France or Switzerland for the weekend and re-enter using my Canadian passport for another 90 days within that same 180 period?
What you are planning to do is break several laws.
As a visitor you are actually not allowed to work in Europe. You are worried that you would have to "turn down jobs in Italy". The reality is that you are not even allowed to accept jobs in Italy.
You intend to take up residence without registering with the local municipality. I know that in the US and other common law countries the municipalities do not keep a population registry, so this may be new to you. In continental Europe when you move to a place you need to register at the local town hall (or whichever local bureaucracy is responsible for this) within a few weeks of your arrival. There they will want to see your long term visa. If the police find out that someone is living somewhere without being properly registered they may come knocking at our door to check you out. If you are found living there without a residence permit you will get an order to leave the country.
And as others have pointed out to you: The whole Schengen area is basically a single country where it comes to visa and passport control. So you can't just pop over the border to France. There normally isn't even a passport check at the border.
So using two passports to get around this is not really going to work, and will still be breaking the law.
You'll need to get permission to take up residence in Italy before you actually do so. Without that permission, you'll only be able to spend half of your time in the entire Schengen area, 90 days out of every 180. That means that every day you spend in France or Spain or Poland, etc., etc., is a day you can't spend in Italy.
Having two passports might help you get away with violating the law, but it might not, and it certainly doesn't change the application of the law, which is that the restriction applies to you, personally, as a non-EU citizen, regardless of which non-EU passport you present.