Understanding the origin of electron–phonon coupling in lead halide perovskites is key to interpreting and leveraging their optical and electronic properties. Here we show that photoexcitation drives a reduction of the lead–halide–lead bond angles, a result of deformation potential coupling to low-energy optical phonons. We accomplish this by performing femtosecond-resolved, optical-pump–electron-diffraction-probe measurements to quantify the lattice reorganization occurring as a result of photoexcitation in nanocrystals of FAPbBr₃. Our results indicate a stronger coupling in FAPbBr₃ than CsPbBr₃. We attribute the enhanced coupling in FAPbBr₃ to its disordered crystal structure, which persists down to cryogenic temperatures. We find the reorganizations induced by each exciton in a multi-excitonic state constructively interfere, giving rise to a coupling strength that scales quadratically with the exciton number. This superlinear scaling induces phonon-mediated attractive interactions between excitations in lead halide perovskites.