Aqueous foams, like other macroscopically divided materials, display intriguing rheological properties. The bubble-scale structure allows for the existence of frozen stresses within the material which can not spontaneously relax by thermal activation. Upon shearing, the system undergoes a series of plastic events which irreversibly modify this internal stress pattern. Reversely, the internal state of the material controls to a large extent its mechanical response to shear. To study this coupling, we have used a two-dimensionally confined aqueous foam along with a numerical simulation. Through image analysis of the film network, we can simultaneously probe the plastic flow and the frozen stress field dynamics under quasi-static shearing. We show that under oscillatory shear of moderate amplitude, the foam experiences a structural relaxation that leads to a decrease of the shear modulus and the emergence of normal stress differences. Upon continous shear, a shear-banding instability is observed, which coincides with the emergence of spatial heterogeneities in the internal stress field characteristics. The dynamics of the internal stress field can be interpreted using a simple statistical model.