We often go in May and have found that, while the weather during the day is usually lovely and warm, there is always the chance of rain for a couple of days in the week. Also, the evenings can be cool and you will need light jackets if yo are eating out.
The weather in June is generally much more settled without having the intense heat of July and August but even in June you may have the odd cloudy day.
Personally, I much prefer the first two weeks of September for a perfect break. The madness and overcrowding of late July and August has died down by then but the weather is still great.