We present the first sizable grammar written for TAG. We present the linguistic coverage of our grammar, and explain the linguistic reasons which lead us to choose the particular representations. We show that TAG formalism provides sufficient constraints for handling most of the linguistic phenomena, with minimal linguistic stipulations. We first state the basic structures needed for parsing French, with a particular emphasis on TAG's extended domain of locality that enables us to state complex sub-categorization phenomena in a natural way. We then give a detailed analysis of sentential complements, because it has lead us to introduce substitution in the formalism, and because TAG makes interesting predictions. We discuss the different linguistic phenomena corresponding to adjunction and to substitution respectively. We then move on to support verb constructions, which are represented in a TAG in a simpler way than the usual double analysis. It is the first time support verb constructions are handled in a parser. We lastly give an overview of the treatment of adverbs, and suggest a treatment of idioms which make them fall into the same representations as 'free' structures.