Ever since the publication of Laviosa’s (1998a; 1998b) pioneering work, the study of lexico-syntactic simplification has held centre stage in corpus translation research concerned with the typical features of translated texts. The simplification hypothesis states that translated texts are simpler than non-translated texts. The convergence hypothesis, also discussed by Laviosa (1998a; 1998b), but less so in follow-up studies, is that translated texts are more homogeneous than original texts, that is they display less variance. To date, simplification has mostly been operationalised in CBTS as type-token ratio, lexical density, core vocabulary coverage, list head coverage and average sentence length. Relying on these parameters, previous research has produced mixed results, with simplification varying across translation modalities, language pairs and registers. The present article sets out to revisit the simplification and convergence hypotheses through the lens of NLP-informed readability research. In particular, we rely on a larger set of simplification indicators and make use of multivariate statistical techniques. We present a simplification study of Europarl corpus data in French translated from English and in non-translated French. The results show that translated French is simpler than original French, lexically and syntactically. We also find evidence of convergence that shows that translators smooth out cross-speaker lexical heterogeneity in translated parliamentary proceedings.