It's almost 7 hours if you were to drive it, so a car or bus won't be faster. I think the problem is there is no real direct route, you kind of have to go around. But to fly I think you'd need to get to a larger airport - Lyon or Geneva so by the time you take a train to one of those cities, then get from the train station to the airport (figure an hour, even though the airport to train station tram is only half an hour, you still have to walk to it, and wait for it). Then you need to be at the airport two hours before the flight. Then once you get to Nice you have to get to the city center to get a train to Antibes. I think unfortunately it is going to take you all day. When I'm in a situation like that, if the total trip itinerary allows, I break it up with a stay somewhere in between.