The weakly supervised audio-visual video parsing (AVVP) task aims to parse a video into a set of modality-wise events (i.e., audible, visible, or both), recognize categories of these events, and localize their temporal boundaries. Given the prevalence of audio-visual synchronous and asynchronous contents in multi-modal videos, it is crucial to capture and integrate the contextual events occurring at different moments and temporal scales. Although some researchers have made preliminary attempts at modeling event semantics with various temporal lengths, they mostly only perform a late fusion of multi-scale features across modalities. A comprehensive cross-modal and multi-scale temporal fusion strategy remains largely unexplored in the literature. To address this gap, we propose a novel framework named Audio-Visual Fusion Architecture Search (AVFAS) that can automatically find the optimal multi-scale temporal fusion strategy within and between modalities. Our framework generates a set of audio and visual features with distinct temporal scales and employs three modality-wise modules to search multi-scale feature selection and fusion strategies, jointly modeling modality-specific discriminative information. Furthermore, to enhance the alignment of audio-visual asynchrony, we introduce a Position- and Length-Adaptive Temporal Attention (PLATA) mechanism for cross-modal feature fusion. Extensive quantitative and qualitative experimental results demonstrate the effectiveness and efficiency of our framework.