This is a competitive application. The doctoral schools offer PhD positions for the best ranked students of each master program. MSIAM typically gets 3 positions.
The fellowship, though granted by doctoral schools, actually come from the French Ministry for Education and Research.
In principle the students at Ensimag and UGA IM2AG apply to the MSTII doctoral school.
CNRS offers so-called BDI PhD Fellowships http://www.dgdr.cnrs.fr/drh/emploi-nonperm/formation.htm
There is no call for application. The applicant must register to a doctoral school, contact a laboratory, define his/her project and apply to the BDI fellowship.
The PhD project may (but does not have to) include some industrial partner.
A small number of PhD positions are offered by Inria https://www.inria.fr/en/centre/sophia/overview/offers/phd-positions/phd-positions
Inria offers a closed list of PhD positions. If you want to define your own PhD project in association with some Inria researcher to make it eligible (i.e. in the closed list), it probably has to be prepared one year before the beginning of the PhD.
Quite a lot of other public research institutes have PhD positions, among which CEA, INSERM, INRA and IRSTEA.
A CIFRE PhD is a tripartite agreement signed by the PhD student, an industrial and a research laboratory.
All the CIFRE PhDs are managed by the ANRS
Research achieved during a CIFRE PhD will be applied research on a subject proposed by an industrial. The approach will thus be clearly a scientific approach as in any thesis but concrete fallouts are expected by the industrial partner.
Works could result in concrete applications, publications in journals or conferences and/or patent registration.
The 71 universities in France each have their own calls to projects for research. Groups of researchers from different labs get support for specific projects, which often include 1 or 2 PhD fellowships.
This used to be the case of Labex (groups of laboratories).
The Rhône-Alpes Region allocates doctoral research grants every year. Its 8 Academic Research Communities (Communautés Académiques de Recherche [ARC]) also finance doctoral dissertations in subjects corresponding to their specialties. We are typically involved in ARC 6 Theme 2: Dispositifs, systèmes, calcul et logiciels (http://lig-membres.imag.fr/ledru/ARC6/FicheARC6v3.5.pdf unfortunately in French).
Warning, the grant is requested by the advisor (AAP=“Project Call” quite early Feb or March -> ask your MSc thesis advisor)
Once hired into a PhD position, you can subscribe to different variants of contract.
One of them makes it possible to receive some training to be a teacher, and to give courses (or lab works or tutorials) at university and receive some additional wages for that.
In our jargon this contract is called DCE or RES (see “Research and Higher Education”) or B contract (!!!) or monitor.