The phone generally waits for an LLDP server to send it an LLDP frame to cue it with the right VLAN to use. FAUCET doesn't do LLDP itself, but, it does of course support doing via NFV. Simply run lldpd on your NFV host, and configure the NFV interface to be in the same untagged (native) VLAN as the port with the phone (the phone's interface will have both tagged and native configuration).
You will also have to specify "drop_lldp: False" in the datapath section of FAUCET's config, to tell FAUCET not to drop LLDP by default.
lldpd should have configuration like (to quote the man page - http://manpages.ubuntu.com/