Initially, downloaded the game on a fresh system but it would immediately close on start-up.

The issue is that Uplay is not automatically downloaded with the game but is required in order to run it. I was able to fix this by downloading a more 'recent' Ubisoft title in my library (Far Cry 5, for instance) which installs Uplay. Only then does Far Cry 3 work normally.

For any 32:9 users like me, note that this game seems to have serious UI scaling issues and given its age, things will look off. You can enable forced letterbox mode but even then the icons are quite low-res compared to what you might expect.