Wearable fall detection systems face a fundamental challenge: while gyroscope data provide valuable orientation cues, naively combining raw gyroscope and accelerometer signals can degrade performance due to noise contamination. To overcome this challenge, we present a dual-stream transformer architecture that incorporates (i) Kalman-based sensor fusion to convert noisy gyroscope angular velocities into stable orientation estimates (roll, pitch, yaw), maintaining an internal state of body pose, and (ii) processing accelerometer and orientation streams in separate encoder pathways before fusion to prevent cross-modal interference. Our architecture further integrates Squeeze-and-Excitation channel attention and Temporal Attention Pooling to focus on fall-critical temporal patterns. Evaluated on the SmartFallMM dataset using 21-fold leave-one-subject-out cross-validation, the dual-stream Kalman transformer achieves 91.10% F1, outperforming single-stream Kalman transformers (89.80% F1) by 1.30% and single-stream baseline transformers (88.96% F1) by 2.14%. We further evaluate the model in real time using a watch-based SmartFall App on five participants, maintaining an average F1 score of 83% and an accuracy of 90%. These results indicate robust performance in both offline and real-world deployment settings, establishing a new state-of-the-art for inertial-measurement-unit-based fall detection on commodity smartwatch devices.