Recent experimental observations of Weyl fermions in materials opens a new frontier of condensed matter physics. Based on first-principles calculations, we here discover Weyl fermions in a two-dimensional layered electride material Y$_2$C. We find that the Y 4$d$ orbitals and the anionic $s$-like orbital confined in the interstitial spaces between [Y$_2$C]$^{2+}$ cationic layers are hybridized to give rise to van Have singularities near the Fermi energy $E_{rm F}$, which induce a ferromagnetic (FM) order via the Stoner-type instability. This FM phase with broken time-reversal symmetry hosts the rotation-symmetry protected Weyl nodal lines near $E_{rm F}$, which are converted into the multiple pairs of Weyl nodes by including spin-orbit coupling (SOC). However, we reveal that, due to its small SOC effects, Y$_2$C has a topologically nontrivial drumhead-like surface state near $E_{rm F}$ as well as a very small magnetic anisotropy energy with several ${mu}$eV per unit cell, consistent with the observed surface state and paramagnetism at low temperatures below ${sim}$2 K. Our findings propose that the Brillouin zone coordinates of Weyl fermions hidden in paramagnetic electride materials would fluctuate in momentum space with random orientations of the magnetization direction.
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