Multivariate time series classification is increasingly investigated in space weather research as a means to predict intense solar flare events, which can cause widespread disruptions across modern technological systems. Magnetic field measurements of solar active regions are converted into structured multivariate time series, enabling predictive modeling across segmented observation windows. However, the inherently imbalanced nature of solar flare occurrences, where intense flares are rare compared to minor flare events, presents a significant barrier to effective learning. To address this challenge, we propose a novel Global Cross-Time Attention Fusion (GCTAF) architecture, a transformer-based model to enhance long-range temporal modeling. Unlike traditional self-attention mechanisms that rely solely on local interactions within time series, GCTAF injects a set of learnable cross-attentive global tokens that summarize salient temporal patterns across the entire sequence. These tokens are refined through cross-attention with the input sequence and fused back into the temporal representation, enabling the model to identify globally significant, non-contiguous time points that are critical for flare prediction. This mechanism functions as a dynamic attention-driven temporal summarizer that augments the model's capacity to capture discriminative flare-related dynamics. We evaluate our approach on the benchmark solar flare dataset and show that GCTAF effectively detects intense flares and improves predictive performance, demonstrating that refining transformer-based architectures presents a high-potential alternative for solar flare prediction tasks.