Here we use magnetic resonant x-ray diffraction to study the magnetic order in a $1.5\text{ }\ensuremath{\mu}\text{m}$ EuTe film grown on (111) ${\text{BaF}}_{2}$ by molecular-beam epitaxy. At $\text{Eu}\text{ }{L}_{\text{II}}$ and ${L}_{\text{III}}$ absorption edges, a resonant enhancement of more than two orders was observed for the $\ensuremath{\sigma}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{'}}$ diffracted intensity at half-order reciprocal-lattice points, consistent with the magnetic character of the scattering. We studied the evolution of the $(\frac{1}{2}\frac{1}{2}\frac{1}{2})$ magnetic reflection with temperature. When heating toward the Neel temperature $({T}_{N})$, the integrated intensity decreased monotonously and showed no hysteresis upon cooling again, indicating a second-order phase transition. A power-law fit to the magnetization versus temperature curve yielded ${T}_{N}=9.99(1)\text{ }\text{K}$ and a critical exponent $\ensuremath{\beta}=0.36(1)$, which agrees with the renormalization theory results for three-dimensional Heisenberg magnets. The fits to the sublattice magnetization dependence with temperature, disregarding and considering fourth-order exchange interactions, evidenced the importance of the latter for a correct description of magnetism in EuTe. A value of 0.009 was found for the $(2{j}_{1}+{j}_{2})/{J}_{2}$ ratio between the Heisenberg ${J}_{2}$ and fourth-order ${j}_{1,2}$ exchange constants. The magnetization curve exhibited a round-shaped region just near ${T}_{N}$ accompanied by an increase in the magnetic peak width, which was attributed to critical scattering above ${T}_{N}$. The comparison of the intensity ratio between the $(\frac{1}{2}\frac{1}{2}\frac{1}{2})$ and the $(1\frac{1}{2}1\frac{1}{2}1\frac{1}{2})$ magnetic reflections proved that the ${\text{Eu}}^{2+}$ spins align within the (111) planes, and the azimuthal dependence of the $(\frac{1}{2}\frac{1}{2}\frac{1}{2})$ magnetic peak is consistent with the model of equally populated S domains.