Laser-plasma accelerators deliver high-charge quasi-monoenergetic electron beams with properties of interest for many applications. Their angular divergence, limited to a few mrad, permits one to generate a small γ ray source for dense matter radiography, whereas their duration (few tens of fs) permits studies of major importance in the context of fast chemistry for example. In addition, injecting these electron beams into a longer plasma wave structure will extend their energy to the GeV range. A GeV laser-based accelerator scheme is presented; it consists of the acceleration of this electron beam into relativistic plasma waves driven by a laser. This compact approach (centimetres scale for the plasma, and tens of meters for the whole facility) will allow a miniaturization and cost reduction of future accelerators and derived X-ray free electron laser (XFEL) sources.