Fusing side information in session-based recommendation is crucial for improving the performance of next-item prediction by providing additional context. Recent methods optimize attention weights by combining item and side information embeddings. However, semantic heterogeneity between item IDs and side information introduces computational noise in attention calculation, leading to inconsistencies in user interest modeling and reducing the accuracy of candidate item scores. These methods also often fail to leverage session-based re-interaction patterns, limiting improvements in score prediction during the decoding phase. To address these challenges, we propose ScoreNet, a consistency-driven framework with multi-side information fusion for session-based recommendation. ScoreNet explicitly models users' persistent preferences, generating consistent decoding scores for candidate items within a unified framework. It incorporates a multi-path re-engagement network to capture re-interaction behavior patterns in a semantic-agnostic manner, enhancing side information fusion while avoiding semantic interference. Additionally, a position-enhanced consistent scoring network redistributes attention scores within sessions, improving prediction accuracy, especially for items with limited interactions. Extensive experiments on three real-world datasets demonstrate that ScoreNet outperforms state-of-the-art models.