This paper presents GeoContrastNet, a language-agnostic framework to structured document understanding (DU) by integrating a contrastive learning objective with graph attention networks (GATs), emphasizing the significant role of geometric features. We propose a novel methodology that combines geometric edge features with visual features within an overall two-staged GAT-based framework, demonstrating promising results in both link prediction and semantic entity recognition performance. Our findings reveal that combining both geometric and visual features could match the capabilities of large DU models that rely heavily on Optical Character Recognition (OCR) features in terms of performance accuracy and efficiency. This approach underscores the critical importance of relational layout information between the named text entities in a semi-structured layout of a page. Specifically, our results highlight the model's proficiency in identifying key-value relationships within the FUNSD dataset for forms and also discovering the spatial relationships in table-structured layouts for RVLCDIP business invoices. Our code and pretrained models will be accessible on our official GitHub.