With respect to discourse organisation, the most basic way of signalling the speaker's or writer's intentions is to use explicit lexical markers: so-called discourse markers or discourse connectives. While a lexicon of discourse connectives associated with the relations they express can be very useful for researchers, especially in Natural Language Processing, few projects aim at collecting them exhaustively, and only in a small number of languages. We present LEXCONN, a French lexicon of 328 discourse connectives, collected with their syntactic categories and the discourse relations they convey, and the methodology followed to build this resource. The lexicon has been constructed manually, applying systematic connective and relation identification criteria, using the Frantext corpus as empirical support. Each connective has been associated to a relation within the framework of Segmented Discourse Representation Theory. We make a case for a few refinements in the theory, based on cases where no existing relation seemed to match a connective's usage.