Innovation is one of the many challenges raised by the digitalization of business and economy. In the current competitive environment, businesses are characterized by radical transformations through digitalization of services and products and their ability to innovate is increasingly linked to the exploration and exploitation of information and communication technologies (ICTs). This paper investigates the role of information systems (IS) as a key factor to innovation capacity. Starting from these issues, the paper explores through an interpretative study of the IS innovation practices as well as perceptions by managers within a sample of 7 French based companies from various industries. The interviews have been conducted on with a guide built based on a framework on IS innovation capacity maturity. Consistently with the framework, the interview guide addresses process areas and practices related to three core categories: management, innovation engineering, and support. The study reveals 7 fundamental contradictions that can explain the main tendencies observed across the companies, out of which the most striking is a generalized lack of maturity when it comes to exploiting their Information Systems to foster innovation.