score:2
That's a rather circuitous route.
This itinerary has two stops inside the Schengen zone: one in Rome and another in Paris. For immigration purposes, the flight from Rome to Paris is treated as a "domestic" flight. You will need to go through immigration to enter the Schengen area in Rome, then go through exit immigration to leave the area in Paris.
Accordingly, you will not just need an airport transit visa for this trip; you'll need a full Schengen visa.