This paper investigates the relationship between competition and innovation at the firm level. Recent papers (Aghion et al., 2005; Askenazy et al., 2013; Rafique Hashmi, 2013) advocate a non-linear relationship, conciliating the Schumpeterian and Arrowian views. In this paper, the effect of competition on innovation is studied at the firm level using a large dataset for France coming from the annual surveys on R&D, covering the period 2000-2013, where a dummy variable is available for product or process innovation. The econometric results do not confirm the inverted-U shape relationship between the Lerner index and innovation, found by Aghion et al. (2005). This may be due to the use of firm-level data rather than industry-level data. However, for most firms, there is a negative effect of competition on innovation, meaning that more competition in the industry or a small market share has a negative effect on the propensity to innovate, either in products or processes, and the effect seems to be slightly stronger for product than for process innovation.