Probing strong-field quantum electrodynamics (QED) is emerging as a promising discovery science area with exciting opportunities. However, while research programs are under evelopment worldwide, reaching the strong-field QED regime still remain a considerable challenge. In this proposal, we aim at exploring novel concepts to reach this goal. Using the PW-class APOLLON laser, we propose to produce high-energy electron beams and strong fields. Our approaches are based on a simple setup and an efficient use of the laser energy. First, high-energy electron beams, exceeding the GeV, will be delivered by a laser-plasma accelerator (LPA). Then, two concepts will be studied experimentally to generate strong fields. Our first concept uses the electron beam itself as the source of the fields, and a self-focusing dynamics in a sequence of conducting foil targets enables to greatly enhance these fields. Our second concept aims at boosting the intensity of the LPA drive laser at the LPA exit, to then use it to collide with the GeV electron beam. The collision is made possible by the reflection of the LPA drive laser on a plasma mirror. The onset of these processes will be characterised by both electron beam and Compton scattering radiation measurements.