hotel reservations cancellable?

You'll find that this varies from hotel to hotel, and in some cases with how you've booked the room (hotel website vs. third-party website). I use booking.com a lot (though I sometimes end up making my reservation on the hotel's website), and one of the things I like about it is that you can easily find the cancellation policy. On some hotel websites it is not so easy, and it is critical information.

Edited to add: I should also have mentioned that many hotels now offer both flexible (refundable up until X days before arrival date) and non-refundable rates. There can be substantial savings on non-refundable rates if you happen to be booking late. It's a risk I'm not willing to take if I'm planning well in advance, but lots of people opt for apartments these days, and they frequently have substantial cancellation fees, so obviously many people are not bothered by that.

We never book hotels in Paris, or anywhere else, that don't have a cancellation policy. We sometimes use Trivago or hotels.com to see what's available but we always book directly with the hotel and not a third party agency. Some hotels will assist you and correspond with you via email. A few will chat with you online. We always use formal language with hotel staff and not the abbreviations like WWYD or LOL, and sign off with a thank you and our names. Being a bit more formal/polite and showing appreciation for their assistance works wonders and occasionally an upgrade upon arrival. Good luck.

As above, cancellation policies differ by individual hotel. As we plan all of our trips well in advance, I use booking.com for most of our reservations and choose only hotels with the option of free cancellation by a stated date. Tariffs are higher than choosing a non-refundable option but I'm unwilling to take the risk when booking as far out as I do. LOL, I'm also covered if I have a momentary brain burp and book for the wrong date!

We just got back from a sidetrip from Paris -- all of our hotel arrangements involved a choice of cancellable reservations or not. It is more expensive generally to have a reservation that can be cancelled; often you get a good deal by paying up front. Anything like this is explicit in your reservation.

On the subject of the advisability of making non-cancelable reservations, I’ll throw in that the two times I’ve done it, we actually had to cancel, for reasons I could never have imagined. One was a “brain burp,” as another poster called it, even though I had checked, checked, and rechecked my dates. The lesson I’ve learned is not to be seduced by the prospect of saving a few dollars. You may lose more than you would have saved.