FWIW there are lots of single nationality non Brits flying at BA. Plenty of Dutch pilots (including a few of the trainers on one or two of the senior fleets, ) a few French and Belgians, not sure about Spaniards or Germans but given the size of the pilot force I’d guess there are a few.....(edit to add: there are also plenty of non EU national pilots at BA, working by virtue of family connections e.g. marriage)...it is a fairly diverse place.
As for the other airlines such as Brits at AF..there are the occasional rumours that it may have happened, but nothing I can verify.
My personal opinion is that if I got on a British Airways flight, I would expect to hear British accents from the crew.
...Given the high percentage of BA cabin crew who are not British (recruited in part because of the need for dual or more language speakers on many flights) and given the fact the cabin crew do the majority of the PAs on a normal flight I think you may well end up being disappointed.