Gene regulatory network inference depends on high-quality prior-knowledge, yet curated priors are often incomplete or unavailable across species and cell types. We present GLM-Prior, a genomic language model fine-tuned to predict transcription factor to target gene interactions directly from nucleotide sequence. We integrate GLM-Prior with PMF-GRN, a probabilistic matrix factorization model, to create a dual-stage training pipeline that combines sequence-derived priors with single-cell gene expression data for accurate and interpretable GRN inference. In yeast, we find that GLM-Prior outperforms motif-based and curated priors, and that downstream gene expression based inference adds little additional value, indicating that most regulatory signal is captured directly from sequence. We show that, across yeast, mouse, and human, GLM-Prior consistently improves GRN inference accuracy and generalizes across species, enabling zero-shot transfer between human and mouse without retraining. These results demonstrate that prior-knowledge construction, rather than inference algorithm complexity, is the current bottleneck in GRN modeling, and that future methods should treat expression data as a contextual modulator of a fixed regulatory scaffold, rather than a primary source of structure discovery.