This work focuses on fast-slow coupled forward-backward stochastic differential equations (FBSDEs). Firstly, the well-posedness of such systems is established and some necessary estimates are provided. Subsequently, the averaging principle with strong convergence for both forward and backward components is established by using Khasminskii's time discretization technique. Finally, this averaging principle is applied to examine the singularly perturbed linear-quadratic stochastic control problem.