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Multilayers based on quantum materials (complex oxides, topological insulators, transition-metal dichalcogenides, etc) have enabled the design of devices that could revolutionize microelectronics and optoelectronics. However, heterostructures incorporating quantum materials from different families remain scarce, while they would immensely broaden the range of possible applications. Here we demonstrate the large-scale integration of compounds from two highly-multifunctional families: perovskite oxides and transition-metal dichalcogenides (TMDs). We couple BiFeO$_3$, a room-temperature multiferroic oxide, and WSe$_2$, a semiconducting two-dimensional material with potential for photovoltaics and photonics. WSe$_2$ is grown by molecular beam epitaxy and transferred on a centimeter-scale onto BiFeO$_3$ films. Using angle-resolved photoemission spectroscopy, we visualize the electronic structure of 1 to 3 monolayers of WSe$_2$ and evidence a giant energy shift as large as 0.75 eV induced by the ferroelectric polarization direction in the underlying BiFeO$_3$. Such a strong shift opens new perspectives in the efficient manipulation of TMDs properties by proximity effects.