Divergence of syntactic structures between languages constitutes a major challenge in using linguistic structure in Machine Translation (MT) systems. Here, we examine the potential of semantic structures. While semantic annotation is appealing as a source of cross-linguistically stable structures, little has been accomplished in demonstrating this stability through a detailed corpus study. In this paper, we experiment with the UCCA conceptual-cognitive annotation scheme in an English-French case study. First, we show that UCCA can be used to annotate French, through a systematic type-level analysis of the major French grammatical phenomena. Second, we annotate a parallel English-French corpus with UCCA, and quantify the similarity of the structures on both sides. Results show a high degree of stability across translations, supporting the usage of semantic annotations over syntactic ones in structure-aware MT systems.