Medical vision-language pre-training (VLP) offers significant potential for advancing medical image understanding by leveraging paired image-report data. However, existing methods are limited by $\textbf{Fa}$lse $\textbf{Ne}$gatives (FaNe) induced by semantically similar texts and insufficient fine-grained cross-modal alignment. To address these limitations, we propose FaNe, a semantic-enhanced VLP framework. To mitigate false negatives, we introduce a semantic-aware positive pair mining strategy based on text-text similarity with adaptive normalization. Furthermore, we design a text-conditioned sparse attention pooling module to enable fine-grained image-text alignment through localized visual representations guided by textual cues. To strengthen intra-modal discrimination, we develop a hard-negative aware contrastive loss that adaptively reweights semantically similar negatives. Extensive experiments on five downstream medical imaging benchmarks demonstrate that FaNe achieves state-of-the-art performance across image classification, object detection, and semantic segmentation, validating the effectiveness of our framework.