Correct, you will not need a test to enter Italy from France after Mar 1 if you're fully vaccinated. You will need to fill in an EU dPLF prior to flying to Italy on this website:
https://app.euplf.eu/#/
The form must be filled in and submitted online, and one can do it even a few weeks before one's trip. I'm not familiar with France's current entry requirements, but they seem to use the same type of EU dPLF, also available from this website.