Answer
Bromide is replaced over fluoride because it is a better leaving group.
Work Step by Step
Bromide is a much larger atom than fluoride, as it is lower on the periodic table and therefore has a larger atomic radius. Consequently, bromide can stabilize a negative charge better and is a weaker base. The weaker the base, the better the leaving group. This can also be determined by relative pKa of conjugate acids: HBr has a lower pKa than HF so it has a weaker conjugate base.