Ferroelectric and ferromagnetic orders rarely coexist, and magnetoelectric coupling is even more scarce. A possible avenue for combining these orders is by interface design, where orders formed at the constituent materials can overlap and interact. Using a combination of magnetotransport and scanning superconducting quantum interference device measurements, we explore the interactions between ferroelectricity, magnetism, and the two-dimensional electron system (2DES) formed at the novel ${\mathrm{LaAlO}}_{3}/{\mathrm{EuTiO}}_{3}/{\mathrm{Sr}}_{0.99}{\mathrm{Ca}}_{0.01}{\mathrm{TiO}}_{3}$(001) heterostructure. We find that the electrons at the interface experience magnetic scattering appearing along with a diverging Curie-Weiss-type behavior in the ${\mathrm{EuTiO}}_{3}$ layer. The 2DES is also affected by the switchable ferroelectric polarization at the ${\mathrm{Sr}}_{0.99}{\mathrm{Ca}}_{0.01}{\mathrm{TiO}}_{3}$ bulk. While the 2DES interacts with both magnetism and ferroelectricity, we show that the presence of the conducting electrons has no effect on magnetization in the ${\mathrm{EuTiO}}_{3}$ layer. Our results provide a first step towards realizing a new multiferroic system where magnetism and ferroelectricity can interact via an intermediate conducting layer.