Longbow archers can attack targets (that are not in fog cloud) up to 600 feet away, but would do so at disadvantage for targets greater than 150 feet away.
However, if the archer first walks into a fog cloud and then shoots, they would roll normally because advantage and disadvantage cancel out, according to this question:
Since advantage and disadvantage caused in a heavy obscured area cancel out, what effect does it have in combat?
It seems weird that one could quadruple the standard range of archers by casting fog cloud on them. Is that really RAW?
(Next round, the archers would probably have to walk out of the fog cloud to reacquire their target and walk back into it with their movement, otherwise they may be targeting the wrong square.)