Deb,
Renting a car should be OK especially as you drive on the wrong side already however if it is required or not depends upon what you intend to do whilst on the Cote d'Azur. French drivers will probably seem a bit more erratic than those back in the US. Alamo operate out of NCE airport and normally give good interline rates. The route to Villefrance is straight along the Autoroute. Parking should be OK as there is public parking around ( there is free parking on the sea front at Antibes for example ). www.cote.azur.fr has info about specific towns (it will test out your French reading ).
You'll need to check with the car hire company about the licence but I think it should be OK. Not too sure what you mean by proper dress for the area .. do you means at the Sporting Club or in the Cote D'Azur generally. Unfortunately ( or fortunately depending upon your opinion ) the last time I was there the dress code was Ferrari red, McLaren silver or Bennetton blue as it was for the F1 Grand Prix.