In this article, we present a numerical method to model the propagation of a fluid-driven fracture in a poroelastic medium in the finite element framework. We developed a zero-thickness finite element to model the fracture. The fracture propagation is governed by a cohesive zone model. The fluid flow within the crack is described by the lubrication equation and the fluid pressure in the fracture acts as an hydraulic and mechanical boundary condition on the lips of the crack. The bi-dimensional pressure diffusion equation and the equilibrium equation in the surrounding porous medium are fully solved numerically. We compare the results of our numerical model with asymptotic analytical solutions. Our numerical model captures very well the analytical solutions in all the asymptotic propagation regimes. In addition, our zero-thickness element method gives access to a finer description of the fluid diffusion in the porous medium and of its coupled mechanical response.