Inria has dubbed the project Software Heritage and says it will adopt distributed infrastructure in order to ensure long-term availability and reliability.
The initiative has already collated source code from more than 20 million software projects, a total of 2.5 billion unique source files.
Two early partners of the project are Microsoft, and DANS, an institution of the Royal Academy of the Arts and Sciences and the Netherlands Organisation for Scientific Research.
Software Heritage has invited companies and individuals from around the world to join and help the project.
The goal is to build a modern "library of Alexandria" of software, "a unique reference database of all source code, a tool for new software projects and a research instrument for computer science: a societal, technical and scientific challenge".