Does FTDI implement the standard communications device class (CDC) USB protocol?
I need to implement a host on the STM32 to connect the device to an FTDI serial chip. But searches on Google say that when using a library from ST there are problems.
No, they don't implement the common CDC class. Their chips return class and subclass set to 0 with vendor ID 0x0403. On PC this is a separate driver handling this communication.
You can confirm this for example by checking linux sources here: https://github.com/torvalds/linux/blob/master/drivers/usb/serial/ftdi_sio.h