Our flight back from Paris was cancelled at 11pm, along with many others. Easyjet desk said we were on our own and could offer no assistance. I managed to get Eurostar tickets and an hotel room overnight for the 3 of us ( 2 adults, 1 child). They are now rejecting the hotel part of the claim as we didn't book through the Easyjet app. Can they insist we booked through the app? People all around us were trying to, and we couldn't find a room for 3 and I was worried about not finding somewhere!
See https://europa.eu/youreurope/citizens/travel/passenger-rights/air/index_en.htm for an overview of the EU air passenger rights applying in your case.
For a cancellation on the day of the flight itself, the airline is obliged to provide
- rerouting to your destination at no cost for you or (if you so choose) refund of your ticket price, and
- assistance while you wait for your re-routed transport, including meals and accommodation, and
- a standardized cash compensation for your lost time.
They can wiggle out of the cash compensation if the cancellation is due to "extraordinary circumstances" that they truly had no way to avoid. (But airlines are wont to try to use this loophole even in cases that the courts have said are not extraordinary enough, so don't take their words for it). The two other points cannot be wiggled out of.
Since the airline did not in fact provide the assistance you requested, you now have a claim against them for expenses you reasonably incurred as a consequence of their failure to do their duty.
To actually cash in on the claim, you may need to threaten legal process. In theory the "national enforcement body" where you or the airline is located might be able to help telling the airline they did wrong -- but some of them are overworked, and they don't have the authority to force the airline to pay out anyway, so you may end up at the courts all the same.
If you feel up to it, simply sending them a draft complaint for small claims court (thereby proving that you've researched how to do that in your location and are prepared to carry through) will often cause a recalcitrant airline to fold.
Or, if you're not quite that adventurous, you may need to engage a lawyer. There are agencies that specialize in these compensation cases on no-cure/no-pay basis.