The correct translation of verb tenses ensures that the temporal ordering of events in the source text is maintained in the target text. This paper assesses the utility of automatically labeling English Simple Past verbs with a binary discursive feature, narrative vs. non-narrative, for statistical machine translation (SMT) into French. The narrativity feature, which helps deciding which of the French past tenses is a correct translation of the English Simple Past, can be assigned with about 70% accuracy (F1). The narrativity feature improves SMT by about 0.2 BLEU points when a factored SMT system is trained and tested on automatically labeled English-French data. More importantly, manual evaluation shows that verb tense translation and verb choice are improved by respectively 9.7% and 3.4% (absolute), leading to an overall improvement of verb translation of 17% (relative).