France is the largest foreign holder of Italian debt. When the yield rises bond prices go down so holders of those bonds see the value of those assets fall. That's bad news for French banks, which hold $416 billion of Italian debt.
With Italian bond prices falling, that puts pressure on French banks capital. Yields have already started rising on French debt because the bond market wants a higher interest rate due to the French exposure to Italian debt.
And if France loses its AAA credit rating the whole EFSF (EU bailout mechanism) would also lose its AAA borrowing capacity and fall apart. The European debt crisis is just about to escalate to the next more dangerous phase (ie. core Europe).
