The standard FF factors as published by K. French (https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html) are created using CRSP data. If one downloads the (US) factors, the first line in the CSV says:
This file was created by CMPT_ME_BEME_OP_INV_RETS_DAILY using the 202105 CRSP database.
The international factors (Europe, Japan, etc.) on the other hand are created using Bloomberg data:
This file was created using the 202105 Bloomberg database.
We are trying to create FF factors for specific country and we have access to Bloomberg. How would we go about? Is there any information from K. French how he is doing it?