HTTP/3 will be performed using HTTPS:// URLs. The world is full of these
URLs and it has been deemed impractical and downright unreasonable to
introduce another URL scheme for the new protocol. Much like HTTP/2 did not
need a new scheme, neither will HTTP/3.
The added complexity in the HTTP/3 situation is however that where HTTP/2 was a completely new way of transporting HTTP over the wire, it was still based on TLS and TCP like HTTP/1 was. The fact that HTTP/3 is done over QUIC changes things in a few important aspects.
Legacy, clear-text, HTTP:// URLs will be left as-is and as we proceed
further into a future with more secure transfers they will probably become
less and less frequently used. Requests to such URLs will simply not be
upgraded to use HTTP/3. In reality they rarely upgrade to HTTP/2 either, but
for other reasons.
The first connection to a fresh, not previously visited host for a HTTPS:// URL probably has to be done over TCP (possibly in addition to a parallel attempt to connect via QUIC). The host might be a legacy server without QUIC support or there might be a middle box in between setting up obstacles preventing a QUIC connection from succeeding.
A modern client and server would presumably negotiate HTTP/2 in the first handshake. When the connection has been setup and the server responds to a client HTTP request, the server can tell the client about its support of and preference for HTTP/3.