If your cordless phones were working before you switched to Verizon FIOS, then it is not your phones that's the problem. Also, your phones are not capable of generating the message from Verizon, Verizon is the one who generates this message. If Verizon messed with any wires, etc., it sounds like something got messed up.
Unplug your phone (base) from the phone jack(s) and the power outlet for
5 minutes and then plug back in, after that test and see if you have
the same results.
Also, try plugging the corded phone in the same phone jack as your cordless is/was plugged into and see if it still has a problem. You could also try plugging your cordless phone into where the corded phone was and trying this as well. I’m happy to help further over the phone at https://www.6ya.com/expert/jeremy_69f3cc28d95bf514