In this study, we investigate interaction-based neural matching models for ad-hoc cross-lingual information retrieval (CLIR) using cross-lingual word embeddings (CLWEs). With experiments conducted on the CLEF collection over four language pairs, we evaluate and provide insight into different neural model architectures, different ways to represent query-document interactions and word-pair similarity distributions in CLIR. This study paves the way for learning an end-to-end CLIR system using CLWEs.