I've never heard of French and Italian mandolin, maybe because I'm not as familiar with classical mandolin as I should be. The only (standard) mando tuning I know of is just like a violin, though doubled, of course. And I know classical mandolins are generally bowlback with an oval soundhole rather than the carved top mandolins with F holes that are typically used in bluegrass and jazz and such.
What does the French and Italian refer to?