Traveling to Europe late May thru late June

Hello,

A friend and I plan on traveling europe for a month between May and
June (arriving the weekend of May 22nd...). We plan to start in
Paris, and then work our way to Munich, and some of the major cities
in Italy (venice, florence, rome). We'll be leaving late June.

We were planning on finding accommodations when we get there, to allow
more flexibility. We looked into reserving the first couple of nights
in Paris, and the first hotel we tried is already booked up for that
weekend! (late May). It being only early April now... we're starting
to wonder if it's necessary to book way in advance these days?

Does anyone have any experience and advice? Searching through the
archives, it seems like most people do not have a problem traveling
without reservations, even during the summer. I'm just wondering
whether we should be concerned, and if hotels are filling up more
quickly nowadays. I guess the fact that the hotel we wanted is
already booked up this far in advance was a bit disheartening.

Another thought I had was... perhaps it's easier to book last minute
because people cancel their reservations?

Thanks!