Douglas, the cost level depends to a great degree on the standard of lodging you choose and of course whether you happen to hit a city during the time of a major event. I was told that the Grand Prix in Monte Carlo really ratchets up demand over an extended part of the coast. It affects hotel rates in Nice much more than the Cannes Film Festival. A much smaller festival can tighten things up in the area immediately around it.
I flew into Nice on May 1 last year and spent about 40 days along the coast (traveling almost as far as the Spanish border) and in Provence. I traveled by train and bus. The weather early in my trip was rather changeable. There was one total wash-out of a day that turned quite cool (early May), a second partial day of intense rain that remained warmish (late May) and some other days with scattered showers. There were lots of clouds early in my visit, and I was told by my hotel manager that Nice's weather in May is quite variable in terms of sun/clouds. I don't remember observing many people in the water; I myself am not at all a beach person. The manager said that April weather was often more stable, but we didn't discuss temperature. I don't think the external temperature or the water temperature would be comfortable for swimming in April.
Off-season the mistral (wind) can be a problem in Provence.
I believe peak season in Nice is July/August. [Edited to add: Southern France is likely to be extremely hot at that time of year; it may be great for splashing around in the water, but it is not comfortable for outdoor sightseeing.] Hotel rates seem to be lower in June and certainly are lower in May, subject to variation due to Big Deal Events like the Grand Prix. I did not find Nice expensive at all in May. The city has many hotels, and competition seemed to be keeping costs quite reasonable.
The regional train running along the coast is an easy and cheap way to get around when you want to visit coastal towns (excluding St.-Tropez, which has no rail service). A car is helpful in the hills, but even some hill town are accessible by bus.
You can find day-by-day historical weather statistics on the website timeanddate.com. The data goes back years, so you can get a good sense of the range of weather you might encounter at any time of year. I've linked to Nice's data for May 2018.