This study is based on the writings and teaching of Gustave Guillaume (1883-1960), one of the earliest proponents of what is today called Cognitive Linguistics. It offers (1) a much needed presentation in English of Guillaume's view of the French system, (2) the clarifications added by his successors, and (3) much empirical detail added by the author from his own extensive experience with the material. The word system in this work, as explained in the very first chapter, is intended in the Saussurian sense of a closed set of contrasts. The method is first briefly applied to English, in order to familiarize the reader with the methodological concepts and terminology, and comparisons are made with the general outline of the French system. The major sub-systems of the French verb are analysed in the four central chapters (4-7) entitled Aspect, Voice, Tense, Mood, followed by a chapter on systemic comparison, and two final chapters of detailed analysis of the verbal morphology and its relevance to the cognitive system.