Producing a radiation source that simultaneously combines, compactness, high brightness, femtosecond duration, tunability over the entire x-ray spectrum, and micrometer source size, is a major challenge in x-ray science. Such a source does not exist while it would satisfy the need of a wide variety of applications, and could bring, into a university scale laboratory, a powerful tool to explore the properties of matter. For example, femtosecond x-rays, fully synchronized with laser pulses, can reveal the fastest transient atomic or molecular dynamics. Micrometer source size would provide an unprecedented increase of the space resolution to bring into light structural details in materials for broad applications. High energy radiation, gamma-rays, will allow to radiograph objects opaque for standard x-rays sources. The FENICS project aims at developing the first source gathering these properties. The project is based on the very promising results of a first experiment, performed in summer 2011 at Laboratoire d’Optique Appliquée, where we have demonstrated a method to generate an intense source of high energy x-rays, delivering highly collimated beams, with high brightness, micrometer source size, and femtosecond duration. Our source is relies on an innovative, robust, and very simple scheme of Compton backscattering, where relativistic electrons from a laser plasma accelerator scatter off an intense laser pulse. The goal of the FENICS project is now to exploit the remarkable potential of this novel source. We will demonstrate that it is possible to produce, efficiently and in a dramaticaly simple way, bright femtosecond x-ray beams, emitted from a micrometer source, tunable from the soft x-ray to the gamma-ray range, with compact laser systems. We will as well perform first applications experiments and show that the source can meet the needs of users. The source developed within FENICS will be more than 5 orders of magnitude brighter than similar sources based on large scale accelerators (millions dollars project are funded to develop these sources, mainly in united states) and will have a source size about 100 times smaller. If we now compared with the most recent laser driven x-ray sources in plasmas, such as Betatron radiation, our novel source requires electrons energies more than 100 times lower, it can produce radiation up to 100 times higher, and it offers the possibility to be nearly monochromatic and tunable. The development proposed will therefore be a significant progress and could mark the emergence of a novel generation of x-ray sources. The research program is ambitious but realizable within three years because it is built on preliminary results, and on the experience of our team, composed of dynamic and young researchers, in laser plasma accelerator and x-ray radiation. We apply for the support of the ANR because a dedicated fund is now essential to develop this novel thematic. We are convinced that we are about to produce the most advanced x-ray source ever produced from laser-plasma interaction and this will have a strong impact in the actual context, where many projects are funded to develop sources of femtosecond x-ray radiation and their applications.