Aghion and coauthors put forward a model which exhibits an inverted-U-shape relationship between innovation and competition: competition may increase the innovation profit margin for firms close to the technological frontier (since they escape competition) but strong competition could also reduce incentives to innovate for laggards (disincentive effect). However their analysis does not take firm size into account. This paper explores this link. Our model stresses that size should matter: if innovations are large-scale and costly in the firm's sector or relatively to the size of the firm, competitive shocks have to be large enough to change innovation choices. Using a unique panel of French firms we show an inverted-U-shape relationship that becomes flatter when the relative cost of R&D increases until it vanish altogether for small firms.