Current models of temporality in language are either inaccurate or too complex to be cognitively plausible. We present a cognitive model of the computation of aspect in French. Our approach emphasizes the importance of minimalism for cognitive plausibility: structures and computation are kept simple and combinatorial explosion is avoided. Though the model and its current implementation remain partial for now, our approach opens the way to a generic and cognitively plausible method for the determination of aspect.