not sure about free or CalDAV, but i thought that proton mail was putting in some calendar function, and eteSync also do calendar, however, it is their own protocol (i think), not calDav. check it out though, it may work with an external CalDAV server?
My biggest problem with Proton is the price. Their family plan is $AUD800 (479 Euro) for 2 years at the cheapest price which is obscene. I can get a family plan with the likes of Microsoft (ugh) for just $260/2 years and it includes Office 365 as well.
Yhe family plan is the price of 3 "unlimited" subscriptions, if you don't need unlimited then Mail Plus is far more reasonable at AU$140/2yrs, for one person though.
I do wish they had a "Mail Plus Family" for up to 3 people, would be a good middle ground to get my family to switch.
Proton has a nice UI and works well (I've used it for two years before moving to mailbox.org) but as of 6 months back, I was unable to make it work outside their walled garden.
You can subscribe to proton calendar with any other calendar app, so you can read your calendar via caldav, but I found no way to edit it other than using their app.
I would recommand Proton for a lot of reasons, but if having a caldav calendar matrers to you I don't think Proton is a good option.