In my experience (in the United States), this name has been used almost exclusively by Italian-Americans. It may have started as a nickname for Antonia, but at this point it's treated as its own name - and again, despite looking quite French, is pretty much a dead giveaway that the bearer is of Italian descent.The name itself is a *little* dated, but I still like it. Certainly not the worst thing to be called.
My best friend's name is Antonette and she was named after her father who's names is Anthony. She and I both thought it was just a made up name and everyone- incuding me- tends to think it's an illterate variant of Antoinette so I never thought it was that amazing. But it is uncommon around here so I guess that's a plus.
This is my birth name, although I usually go by the nickname "Toni" (Anne had bad connotations in our family). I was named after my agnate grandmother, who was born in the 1920s. It used to make me cringe when I heard my full name on the first day of class, but I was always complimented on how pretty a name it is. I love it now, because it is so rare and unique in the States, especially in my generation (Gen-Y). Although, I still can get annoyed when people assume it AntoInette and pronounce it thus. There *is no "i"* in my name. It is *not* French! So be prepared for that if you decide to name you kid this in the U.S.
The name itself is a *little* dated, but I still like it. Certainly not the worst thing to be called.