Looking for a very good hotel in Antibes with a pool, close to beach and town, breakfast and parking included. We will be staying May 18th to the 22nd . Prefer to spend under $400 a night.
You'll need a heated pool if you want to swim in Antibes this month. In your price range, you may be able to find one, but I'm not sure they do heated pools much on the Riviera. I know it seems sort of odd, but high season down there is July-August. You can start by taking a look on booking.com. It doesn't look too promising in terms of hotels with the amenities and location you want. You may need to expand your geographical area. It might be worth Googling "heated pool Riviera" to see whether something useful turns up.
I've taken a look at the weather forecast for the next ten days, and the Antibes highs for March 18-20 are projected to be 55F, 47F and 50F. As windy as beaches often are, I don't think I'd particularly even want to walk on the beach at those temperatures.