Quantum critical points separating weak ferromagnetic and paramagnetic phases trigger many novel phenomena. Dynamical spin fluctuations not only suppress the long‐range order, but can also lead to unusual transport and even superconductivity. Combining quantum criticality with topological electronic properties presents a rare and unique opportunity. Here, by means of ab initio calculations and magnetic, thermal, and transport measurements, it is shown that the orthorhombic CoTe2 is close to ferromagnetism, which appears suppressed by spin fluctuations. Calculations and transport measurements reveal nodal Dirac lines, making it a rare combination of proximity to quantum criticality and Dirac topology.