All I know and can find is that you need a regular passport to enter france as an entry point into schengen.
because of the schengen agreement there are almost no passport controls at airports, ports and land crossings any more.
I fly roughly 50 intra EU flights per year and the last time I got my passport checked (for anti terror reasons) was on my flight from berlin to brussels just after the last attacks.
I would give it a try and in case it really does not work try to figure out how to get back home from italy...