Cross-lingual document search is an information retrieval task in which the queries' language differs from the documents' language. In this paper, we study the instability of neural document search models and propose a novel end-to-end robust framework that achieves improved performance in cross-lingual search with different documents' languages. This framework includes a novel measure of the relevance, smooth cosine similarity, between queries and documents, and a novel loss function, Smooth Ordinal Search Loss, as the objective. We further provide theoretical guarantee on the generalization error bound for the proposed framework. We conduct experiments to compare our approach with other document search models, and observe significant gains under commonly used ranking metrics on the cross-lingual document retrieval task in a variety of languages.