UPDATE: 2023: as of the writing of this post there is a relatively new specification RFC9220 for websockets built on top of HTTP3 https://datatracker.ietf.org/doc/rfc9220/ .
- Please note RFC 9220 is a specification and so does not help answer questions like: does web-browser X/Y/Z (or library A/B/C, or operating system D/E/F) support this?
Since this is the top search result for "http3 websockets", I want to keep the answers up-to-date.
As of December 2021, there is now an IETF draft that amends RFC8441 (Bootstrapping WebSockets with HTTP/2) with the adjustments necessary for HTTP/3. If the draft is accepted, there will be a standardized way for WebSockets to be initiated over HTTP/3.
The draft is on its second revision and will expire in July 2022 if there are no further revisions and it is not accepted by that time.