I went interrailing twice before and from my own experience try to avoid August, it's way to hot in the south of europe and in central europe there are a lot og thunderstorms, nearly everyday and it's quite annoying when backpacking!
End of may till july sounds good to me, less people, good weather and people aren't fed up wih tourists yet...Plus, if you plan on going to Scandinavia, their summer ends at the end of july, then the weather is not as good as what it could be in the months before...
And would also like to say that the French do go out of their country, they do travel, but in the summer why go somewhere else when you can stay home for cheaper??
Hope it helps, a random French guy, Nico