The Italian paradox is the idea that Italians live long, healthy lives despite eating lots of carbohydrate-rich food (sometimes referred to more generally as the Mediterranean diet, so as to include other olive-rich countries such as Greece or Cyprus). In practice, on a daily basis one must eat several large meals consisting of bread, pasta and meatballs, but as long as you use olive oil instead of butter and drink lots of red wine, and take afternoon naps, you'll live long enough to become a mafia don.
Of course, the peddlers of this diet would ignore the fact that the number one killer of Italians is heart disease due to high cholesterol levels, which makes belief in the efficacy of this diet the true paradox.
There are parallels to the French paradox, likely because they both refer to European countries with large wine production. The differences in traditional French and Italian cuisines, even taking into account the variety that occurs between different regions of the countries, however, show that those parallels hold very little water.
Odds of this diet helping you? About 1 in 61. One thing the French and Italians do have in common is that they tend to walk (and generally exercise) more than Americans, so a more reliable way to get health benefits using them as an example would be to get out more.