Article 21 of the Schengen Borders Code specifies that
The abolition of border control at internal borders shall not affect [...] (b) the possibility for a Member State to provide by law for an obligation to hold or carry papers and documents [...]
So, strictly speaking, you ought to check with Italy and Greece to see whether they require someone who is entering the country (by way of an internal Schengen border), who holds a residence permit from a Schengen country, to carry a passport in addition to the residence permit.
Also, if either country has a requirement that people generally carry identification, you should check whether your carte de séjour will satisfy that requirement. As an example, it seems that in the Schengen country I'm most familiar with, the Netherlands, it would not.
I looked very briefly at the web site of the Greek diplomatic mission to France (http://www.mfa.gr/france/fr/), and didn't see anything indicating one way or the other. Most information I found on the internet was geared towards travelers entering from outside the Schengen area.
In practice, it is probably sufficient to check with the ferry company. I checked the web site of http://www.greekferries.gr, and didn't find anything, but they do have a page advising that a passport or ID card is necessary to travel with an electronic ticket. Their customer service office ought to be able to tell you whether your carte de séjour will be acceptable as identification.