ANR (Agence Nationale de la Recherche) is the National French Agency for Research. It is an independent  agency created in 2005 that funds scientific teams, both public and private, in the form of short-term research contracts.  In general the idea to fund research on projects is not bad but at present ANR is not working  well in France. The problem has been recently outlined by Fabien Malbet the president of the ANR section for Universe Science[1].  As he pointed out only 8% or 9% of the projects are funded every year,  a success rate lower than the ERC. A so low success rate makes the selection quite arbitrary, it is sufficient a sentence in your project that does not sound good to a reviewer to get a vote slight below the maximum and make your project reject.[2]
Therefore the major part of laboratories and research institutes are obliged to search for other funding sources to survive. There are strong competitions to grab the  few regional funds or to get PhD students from the Ecole Doctorale.[3] In some lab researchers have to find funding also to pay master students that are not funded any more by university.
In this panorama that is slowly degrading, for lack of funds, the only entities that still scrape along are big universities, and “Grandes écoles”  mainly in Paris, thanks to their internal resources.
At the end, ANR is now transforming in a lottery to give researches the hope to get some money.

References:
[1] Président du comité ANR des Sciences de l’Univers: impossible d’avoir une politique scientifique!
[2] L’ANR, le ministre et les démissionnaires
[3] L’open data selon l’ANR