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With more than 300 days of sunshine per year, Provence and the Riviera enjoy France's sunniest weather. Spring and fall are best, with generally comfortable weather — though crowds can be a problem, particularly during holiday weekends and major events (May is worst).
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To complete the full context of the quote, he is isolating it Spring and Fall, with May being the worst due to holiday weekends and major events. I'll not that the context includes the Riviera, which has two large major events in May --- the Cannes Film Festival and the Monaco Grand Prix. The overlap weekend is bad.
That said, I've been surprised with the amount of traffic in May in Western Provence, with not only the French but Americans as well.
My personal worst time to visit would be January, where things are closed down, the Mistral has a chance of blowing, and holidays have passed by. Late June/Early July is another bad time due to the lavendar seeking crowds and the heat.