The Internet has been covered by legal deposit legislation in France since 2006, making web archiving one of the missions of the Bibliothèque nationale de France (BnF). Access to the web archives has been provided in the library on an experimental basis since 2008. In the context of increasing interest in many countries in web archiving and how it may best serve the needs of researchers, especially in the expanding field of Internet studies for social sciences, a qualitative study was performed, based on interviews with potential users of the web archives held at the BnF, and particularly researchers working in various areas related to the Internet. The study aimed to explore their needs in terms of both content and services, and also to analyse different ways of representing the archives, in order to identify ways of increasing their use. While the interest of maintaining the "memory" of the web is obvious to the researchers, they are faced with the difficulty of defining, in what is a seemingly limitless space, meaningful collections of documents. Cultural heritage institutions such as national libraries are perceived as trusted third parties capable of creating rationally-constructed and well-documented collections, but such archives raise certain ethical and methodological questions.