Kayne's (1989) seminal paper on participle agreement in Italian and French has spurred numerous studies on the syntactic conditions governing agreement relations. The focus of this paper is on the semantic aspects of this phenomenon. Within the framework of Chomsky’s Minimalist Program, an analysis of French participle agreement is developed, that relates the semantic impact of overt agreement to the syntactic structure that it enforces. We argue that the interaction of Move with the projection of a morphologically strong AGR-O/v determines the position of DPs at LF and their interpretations. Modifying Diesing’s proposal for a syntax-semantic mapping, we propose that only DPs adjoined to a V-head (incorporation) can be interpreted predicatively (or non-specifically) in the sense of De Hoop (1992) while those adjoined to AGR-O/v projection receive a specific interpretation. We further take the presence of AGR-O/v in a sentence structure to be subject to Economy conditions operating on the numeration. The complex distribution of overt object agreement in French, -- optional in accusative constructions, obligatory in passives and impossible in impersonal constructions -- as well as its semantic impact on the interpretation of the triggering nominal expressions are then shown to derive straightforwardly from the interaction of Case and the Economy driven projection of AGR-O/v in the sentence structure.