RNA polymerase III (Pol III) is an essential enzyme responsible for the synthesis of several small noncoding RNAs, a number of which are involved in mRNA translation. Recessive mutations in POLR3A, encoding the largest subunit of Pol III, cause POLR3-related hypomyelinating leukodystrophy (POLR3–HLD), characterized by deficient central nervous system myelination. Identification of the downstream effectors of pathogenic POLR3A mutations has so far been elusive. Here, we used CRISPR-Cas9 to introduce the POLR3A mutation c.2554A→G (p.M852V) into human cell lines and assessed its impact on Pol III biogenesis, nuclear import, DNA occupancy, transcription, and protein levels. Transcriptomic profiling uncovered a subset of transcripts vulnerable to Pol III hypofunction, including a global reduction in tRNA levels. The brain cytoplasmic BC200 RNA (BCYRN1), involved in translation regulation, was consistently affected in all our cellular models, including patient-derived fibroblasts. Genomic BC200 deletion in an oligodendroglial cell line led to major transcriptomic and proteomic changes, having a larger impact than those of POLR3A mutations. Upon differentiation, mRNA levels of the MBP gene, encoding myelin basic protein, were significantly decreased in POLR3A-mutant cells. Our findings provide the first evidence for impaired Pol III transcription in cellular models of POLR3–HLD and identify several candidate effectors, including BC200 RNA, having a potential role in oligodendrocyte biology and involvement in the disease.