Unless you're able to identify your specific FT232 chip over any others you have to send an init frame to each com port chip on the system and listen for the reply from your product. (or at least every FT232 on the system)
You can code your device to send out a ident packet every so often and then listen for it, but to scan many com ports fast you need this ident packet repeating very fast which can be undesirable.
In one of my products i don't bother checking for FT232 chips, i just enumerate all com ports on the system and cycle through them looking for a responses to my init frame.
I found it to take less than 2sec to check 10 ports for my device with a fast baudrate and a realistic timeout before trying the next port. Is pretty uncommon on a consumer pc/laptop to have more than 4 active com ports so detection speed really isn't a problem at all.
However, one thing you have to be aware of when testing all ports on the PC is potential side effects of probing unknown devices serially with your init string.
It's conceivable you could trigger some response from other devices on the system. It might use up expensive paper (com port printers) or corrupt serial terminals etc..
In my case the product is installed in a car so people are only ever going to be connecting with a laptop. I can be pretty sure no one is going to connect to my product with a $10,000 desktop PC wired to expensive equipment over many serial ports.
So ideally you want to identify your FT232 over all others and eliminated this problem entirely but for general consumer stuff it's usually fine to just cycle through the ports probing for your product.
Side note: Always enumerate the active ports on the system, never loop through trying to open ports from 1 up to X catching/handling the errors from ports that don't exist.
For one things it's really slow, com port numbering is remembered so someones 5 year old laptop maybe up to assigning COM30 to new devices. So you have to scan to quite a high number.
Secondly windows sometimes gets a bit annoyed with you opening/closing ports and throwing exceptions fast like that.
And lastly, its just an ugly way to do it
(I think there was another problem as well, but i cant remember it)