Here are some mailing lists or web sites that announce on a regular basis PhD grants in areas close to the core of the MPRI master. If you are aware of other relevant lists or if you find one of the links below is obsolete or simply not working please write to the Master's director.
In general, all applications to a French PhD School or Foundation require an advisor who is working in a laboratory attached to the School/Foundation and who presents a PhD project and a PhD student.
Paris Center PhD School in Mathematical Sciences
Paris Center PhD School in Computer Science, Electronics, and Telecom
Paris South PhD School in Computer Science
Paris Foundation for Mathematical Sciences (includes PhD)
Sorbonne Université PhD grants for foreign students (usually early deadline)
Mailing list of CNRS-GDR group on Algorithms, Languages, and Programming
INRIA job announcements (includes PhD)
CEA job announcements (includes PhD)
Research positions in Cryptography
IEEE Information theory society job announcements (includes PhD)