Prolonged driver inattention significantly increases the risk of traffic accidents, necessitating continuous physiological monitoring for improved road safety and driver wellbeing. This study proposes a Self-Attention-based Hybrid Quantum Neural Network (SAHQNN), a novel framework integrating trainable Parameterized Quantum Circuits (PQCs) with selective self-attention for automated detection of phone call distraction-induced cognitive and emotional driver inattention from multimodal wearable biosignals. Multimodal physiological signals consisting of single-lead Electrocardiogram (ECG, 256 Hz) and Respiration (RSP, 128 Hz) were acquired from $N=20$ participants under Normal and Distracted-Inattention driving conditions using a textile wearable smart shirt. The Distracted-Inattention condition was induced through a hands-free phone call that simultaneously imposed cognitive load, emotional arousal, and secondary task engagement on the driver through active questioning, reflecting the multidimensional nature of driver inattention beyond speech activity alone. Multi-domain features reduced via Random Forest Feature Importance (RFF) were angle-encoded into 10-qubit PQCs with 20 trainable variational $R_Y\left(\theta \right)$ gates optimized via the parameter-shift rule, establishing inter-qubit correlations through Hadamard and Controlled-NOT (CNOT) entanglement layers. Pauli-Z measurement outputs were processed through a selective self-attention layer, producing Attentive Quantum Features (AQF) that were subsequently classified by fully connected layers. The proposed SAHQNN achieves 77.50% accuracy and 70% weighted F-measure under Leave One Subject Out Cross-Validation (LOSOCV), with statistically significant improvements over all standard classical baselines ($p<0.001$, Cohen’s $d>1.5$) and 61% fewer parameters than the strongest classical competitor, demonstrating the feasibility of parameter-efficient trainable hybrid quantum neural networks for subject-independent driver inattention detection.