I've also been reading about the internal border policies for the Schengen states. It seems like there is really no checks but since I had booked my flight to Milan from Paris in an airport kind of far away from the city I thought it would be best to check to see if I'll actually be allowed to board before going...
It is correct, there is no border patrols between the individual Schengen states. That is the point of the Schengen area and the concept of common unified visa. Theoretically, there should not even be any checks at the airports if you fly from Paris to Milan, but for local security reasons, airports still have some checks before you enter the flight terminal, just to make sure people without tickets do not go there. A passport is not required, a local ID will do, but Schengen zone visitors do not have local IDs, so they show passports. From this perspective, it is safer to travel by train or bus as there is no checks.