Fly into the Nice Côte d'Azur Airport, and rent a vehicle through Europcar, Hertz, or Avis. Rental cars in Europe are typically cheapest when booked by the week with unlimited mileage. A compact car with a collision damage waiver, insurance, and gas will probably run you about $400.
The information here outlines a basic itinerary, but for detailed directions, maps, and mileage calculations, visit viamichelin.com.
The weather in the French Riviera is mild and sunny year-round. December through February are the coldest months, with an average of 56 degrees during the day. May through August are the busiest months for tourists. To avoid peak hotel rates, don't visit in May, when the International Cannes Film Festival and the Monaco Formula 1 Grand Prix are usually held.