The temperature dependence of the relaxation dynamics in the bilayer thin film heterostructure composed of multiferroic BiFeO3 (BFO) and superconducting YBa2Cu3O7 (YBCO) grown on a (001)SrTiO3 substrate is studied by a time-resolved pump-probe technique, and compared with that of pure YBCO thin film grown under the same growth conditions. The superconductivity of YBCO is found to be retained in the heterostructure. We observe a speeding up of the YBCO recombination dynamics in the superconducting state of the heterostructure, and attribute it to the presence of weak ferromagnetism at the BFO/YBCO interface as observed in magnetization data. An extension of the Rothwarf-Taylor model is used to fit the ultrafast dynamics of BFO/YBCO, that models an increased quasiparticle occupation of the ferromagnetic interfacial layer in the superconducting state of YBCO.