We present a relatively large coverage French grammar written with the formalism of Interaction Grammars. This formalism combines two key ideas: the grammar is viewed as a constraint system, which is expressed through the notion of tree description, and the resource sensitivity of natural languages is used as a syntactic composition principle by means of a system of polarities. We give an outline of the expressivity of the formalism by modelling significant linguistic phenomena and we show that the grammar architecture provides for re-usability and tractability, which is crucial for building large coverage resources: a modular source grammar is distinguished from the object grammar which results from the compilation of the first one, and the lexicon is independent of the grammar. Finally, we present the results of an evaluation of the grammar achieved with the LEOPAR parser with a test suite of sentences.