I can see there is a lot of confusion between USB-C and Thunderbolt 3 (or later), which is not surprising, since they use the same port.
However, while you can connect a FireWire device to a Thunderbolt 3 port using a set of adapters (as stated above), you cannot do it with a "regular" USB-C port.
That is not an issue for most Macs, but some have USB-C-only ports (without Thunderbolt capablility) and those will not work with FireWire, no matter what adapters you use. It is not even theoretically possible.
Make sure the USB-C port is also a Thunderbolt port and it will work as expected with the appropriate adapters.