Does one need to know Greek? The Byzantines are obviously such a big part of the period, but I’m mostly interested in Late Antique Africa and Britanny/Francia, whic are Latin speaking both of them. But would I need to know Greek to be competitive after a PhD?
I'm more early medieval than late antiquity, so there may be some variation.
Generally in my field it's advised that you should have either Latin or ancient Greek, for accessing primary material, and then either French or German for accessing secondary material. This is a fairly standard requirement for graduate programs in medieval European history.
Latin would likely be more useful for you than Greek, if you're looking at Brittany/Francia, though I'm not sure about Africa, as I expect that will vary by country. French I think would probably be most important for Brittany/France, in terms of scholarship, though a reading-knowledge of German would undoubtedly be handy.
Depending on how you define late antiquity, you might encounter some Old Breton in your study of Brittany, but I think that's more on the tail-end of your time period, and so is probably not necessary.
Whether or not you'd need to know Greek, I expect, would depend on what you're looking at specifically.